Bernard Helffer

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Bernard Helffer is affiliated with the following schools: Paris-Saclay University, University of Nantes

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According to Wikipedia, Bernard Helffer is a French mathematician, specializing in partial differential equations, spectral theory, and mathematical physics. He is the son of the pianist Claude Helffer and the musicologist Mireille Helffer. Helffer studied from 1968 at the École Polytechnique and received in 1976 from the University of Paris-Sud his doctorate under Charles Goulaouic with dissertation Hypoellipticité pour des classes d'opérateurs pseudodifférentiels à caractéristiques multiples. From 1971 to 1978 he did research at CNRS, from 1978 to 1989 he was a professor at the University of Nantes, and then he was a professor at the University Paris-Sud .

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Bernard Helffer's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Multiple wells in the semi-classical limit I (1984) (450)
Semi-Classical Analysis for the Schrödinger Operator and Applications (1988) (386)
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians (2005) (320)
Magnetic Bottles in Connection with Superconductivity (2001) (199)
Nodal Domains and Spectral Minimal Partitions (2006) (156)
On the correlation for Kac-like models in the convex case (1994) (147)
Eigenvalues Variation. I.: Neumann Problem for Sturm-Liouville Operators (1993) (139)
Semiclassical Analysis for the Ground State Energy of a Schrödinger Operator with Magnetic Wells (1996) (131)
Spectral Theory and its Applications (2013) (123)
Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum (1989) (120)
Spectral Methods in Surface Superconductivity (2010) (96)
Semiclassical Analysis, Witten Laplacians, and Statistical Mechanics (2002) (94)
Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains (1998) (93)
On diamagnetism and de Haas-van Alphen effect (1990) (82)
Quantitative Analysis of Metastability in Reversible Diffusion Processes Via a Witten Complex Approach: The Case With Boundary (2006) (79)
Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian (2006) (75)
Comparaison entre les diverses notions de résonances (1987) (74)
Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3 (2001) (72)
Asymptotic of the density of states for the Schrödinger operator with periodic electric potential (1998) (71)
On spectral minimal partitions : the case of the sphere (2009) (70)
On the Stability of the Relativistic Electron-Positron Field (1999) (69)
Upper critical field and location of surface nucleation of superconductivity (2003) (65)
THE LOG-SOBOLEV INEQUALITY FOR UNBOUNDED SPIN SYSTEMS (1999) (63)
On the Third Critical Field in Ginzburg-Landau Theory (2005) (61)
NUMERICAL SIMULATIONS FOR NODAL DOMAINS AND SPECTRAL MINIMAL PARTITIONS (2010) (59)
Multiple Wells in the Semi‐Classical Limit III ‐ Interaction Through Non‐Resonant Wells (1985) (58)
An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material (1993) (54)
Eigenvalues for the Robin Laplacian in domains with variable curvature (2014) (52)
On Spectral Minimal Partitions: A Survey (2010) (51)
Limiting absorption principle and resonances for the Dirac operator (1992) (49)
Magnetic bottles for the Neumann problem: The case of dimension 3 (2002) (48)
Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture II (1990) (47)
Compactness of the solution operator to ∂¯ in weighted L2-spaces☆ (2007) (47)
From resolvent bounds to semigroup bounds (2010) (45)
REMARKS ON DECAY OF CORRELATIONS AND WITTEN LAPLACIANS BRASCAMP-LIEB INEQUALITIES AND SEMICLASSICAL LIMIT (1998) (44)
Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses (2014) (42)
Aharonov–Bohm Hamiltonians, isospectrality and minimal partitions (2009) (40)
Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities (1999) (40)
DEGENERATE PARABOLIC OPERATORS OF KOLMOGOROV TYPE WITH A GEOMETRIC CONTROL CONDITION (2015) (38)
Riesz means of bound states and semiclassical limit connected with a Lieb–Thirring's conjecture (1990) (38)
Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: Analysis near the bottom (2008) (36)
On a magnetic characterization of spectral minimal partitions (2013) (35)
Tunneling between corners for Robin Laplacians (2014) (34)
Nodal and spectral minimal partitions -- The state of the art in 2015 -- (2015) (33)
Semiclassical spectral asymptotics for a two-dimensional magnetic Schr\"odinger operator: The case of discrete wells (2010) (32)
The Distribution of Surface Superconductivity Along the Boundary: On a Conjecture of X. B. Pan (2007) (32)
Tunneling for the Robin Laplacian in smooth planar domains (2015) (32)
Nonlinear eigenvalues and analytic hypoellipticity (2002) (32)
Around the Transfer Operator and the Trotter-Kato Formula (1995) (30)
On Spectral Theory for Schrödinger Operators with Magnetic Potentials (1994) (30)
On nodal domains in Euclidean balls (2015) (29)
Numerical Analysis of Nodal Sets for Eigenvalues of Aharonov–Bohm Hamiltonians on the Square with Application to Minimal Partitions (2011) (29)
Walk inside Hofstadter's butterfly (1989) (29)
Energy asymptotics for Type II superconductors (2005) (29)
On the Spectrum of Non-Selfadjoint Schrödinger Operators with Compact Resolvent (2014) (28)
Superconductivity between HC2 and HC3 (2010) (28)
The Montgomery model revisited (2010) (27)
Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator II: The Case of Degenerate Wells (2010) (27)
REMARKS ON DECAY OF CORRELATIONS AND WITTEN LAPLACIANS II — ANALYSIS OF THE DEPENDENCE ON THE INTERACTION (1999) (27)
Accurate Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator (2013) (26)
Around a stationary phase theorem in large dimension (1994) (26)
Converse Spectral Problems for Nodal Domains (2007) (26)
Strong diamagnetism for general domains and application (2007) (26)
Courant-Sharp Eigenvalues for the Equilateral Torus, and for the Equilateral Triangle (2015) (26)
ON MATHEMATICAL MODELS FOR BOSE–EINSTEIN CONDENSATES IN OPTICAL LATTICES (2008) (25)
On the Hartree-Fock Equations of the Electron-Positron Field (2004) (25)
On Spectral Properties of the Bloch-Torrey Operator in Two Dimensions (2016) (25)
On the Ginzburg‐Landau critical field in three dimensions (2007) (24)
Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in $${\mathbb{R}^2}$$ (2010) (24)
Magnetic wells in dimension three (2015) (24)
NODAL DOMAINS IN THE SQUARE—THE NEUMANN CASE (2014) (23)
Semiclassical Spectral Asymptotics for a Magnetic Schrödinger Operator with Non-vanishing Magnetic Field (2013) (23)
Nodal sets for the groundstate of the Schrödinger operator with zero magnetic field in a non simply connected domain (2007) (23)
Nodal minimal partitions in dimension 3 (2010) (23)
On minimal partitions: New properties and applications to the disk (2010) (23)
Sturm’s theorem on zeros of linear combinations of eigenfunctions (2017) (23)
Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field (2012) (22)
A Proof of the Bott Inequalities (1988) (22)
Spectral properties of higher order anharmonic oscillators (2009) (22)
The Ginzburg–Landau Functional with Vanishing Magnetic Field (2014) (21)
The Ginzburg–Landau equations in a semi-infinite superconducting film in the large κ limit (1997) (21)
Nodal Sets, Multiplicity and Superconductivity in Non-simply Connected Domains (2000) (21)
ON PSEUDO-SPECTRAL PROBLEMS RELATED TO A TIME-DEPENDENT MODEL IN SUPERCONDUCTIVITY WITH ELECTRIC CURRENT (2011) (21)
Spectral properties of the Kac operator in large dimension (1995) (20)
Global Stability of the Normal State of Superconductors in the Presence of a Strong Electric Current (2013) (20)
The Complex Airy Operator on the Line with a Semipermeable Barrier (2016) (20)
Eigenvalues variation. II: Multidimensional problems (1993) (20)
Splitting in large dimension and infrared estimates. II. Moment inequalities (1998) (20)
Long-time vanishing properties of solutions of some semilinear parabolic equations (2001) (19)
A review on large k minimal spectral k-partitions and Pleijel's Theorem (2015) (19)
RIGOROUS RESULTS FOR THE GINZBURG-LANDAU EQUATIONS ASSOCIATED TO A SUPERCONDUCTING FILM IN THE WEAK κ LIMIT (1996) (18)
A. Stern’s analysis of the nodal sets of some families of spherical harmonics revisited (2014) (18)
Minimal partitions for anisotropic tori (2014) (18)
On a family of solutions of the second Painlevé equation related to superconductivity (1998) (17)
Spectral semi-classical analysis of a complex Schr\"odinger operator in exterior domains (2017) (17)
Introduction to semi-classical methods for the Schrödinger operator with magnetic field (2016) (16)
Chambers’s Formula for the Graphene and the Hou Model with Kagome Periodicity and Applications (2014) (16)
Nodal domain theorems à la Courant (2004) (16)
Optimal Uniform Elliptic Estimates for the Ginzburg-Landau System (2006) (15)
Remarks on two notions of spectral minimal partitions (2009) (15)
Remarks on the boundary set of spectral equipartitions (2012) (14)
On semi-classical questions related to signal analysis (2010) (14)
On the absence of a first order correction for the number of bound states of a Schrödinger operator with Coulomb singularity (1992) (14)
Stability of Bifurcating Solutions for the Ginzburg-Landau Equations (1998) (14)
Reduced Landau–de Gennes functional and surface smectic state of liquid crystals (2008) (14)
Proof of the De Gennes formula for the superheating field in the weak κ limit (1997) (14)
Asymptotic methods for the eigenvalues of the Rayleigh equation for the linearized Rayleigh-Taylor instability (2003) (13)
Nodal sets of eigenfunctions, Antonie Stern’s results revisited (2014) (13)
On a Schrödinger operator with a purely imaginary potential in the semiclassical limit (2017) (13)
Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality (2015) (13)
The density of superconductivity in domains with corners (2017) (13)
Semiclassical Analysis for the Schrödinger Operator with Magnetic Wells (After R. Montgomery, B. Helffer-A. Mohamed) (1997) (12)
Superconductivity near the Normal State in A Half-Plane under the Action of A Perpendicular Electric Current and an Induced Magnetic Field, Part II: The Large Conductivity Limit (2012) (12)
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field (1998) (12)
Eigenvalue estimates for a three-dimensional magnetic Schrödinger operator (2012) (12)
On the total bandwidth for the rational Harper's equation (1995) (12)
On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator (2016) (11)
Sharp trace asymptotics for a class of 2D-magnetic operators (2011) (11)
Universal estimate of the gap for the Kac operator in the convex case (1994) (11)
Semiclassical asymptotics and gaps in the spectra of periodic Schr (2006) (11)
Splitting in Large Dimension and Infrared Estimates (1997) (11)
Semiclassical analysis of Schr\"odinger operators with magnetic wells (2008) (11)
Strong diamagnetism for general domains and applications (2006) (11)
h-PSEUDODIFFERENTIAL OPERATORS AND APPLICATIONS: AN INTRODUCTION (1997) (10)
The weak Pleijel theorem with geometric control (2015) (10)
Criteria to the Poincaré inequality associated with Dirichlet forms in ℝd, d ≥ 2 (2003) (10)
Inequalities for the lowest magnetic Neumann eigenvalue (2017) (10)
Spectral gaps for periodic Schr\"odinger operators with hypersurface magnetic wells (2008) (10)
Mixed Normal-Superconducting States in the Presence of Strong Electric Currents (2015) (10)
Partial differential equations on nilpotent groups (1984) (9)
A Beals criterion for magnetic pseudo-differential operators proved with magnetic Gabor frames (2018) (9)
Pleijel’s theorem for Schrödinger operators with radial potentials (2016) (9)
Remarks on the Mittleman max?min variational method for the electron-positron field (2006) (9)
BULK SUPERCONDUCTIVITY IN TYPE II SUPERCONDUCTORS NEAR THE SECOND CRITICAL FIELD (2008) (9)
On spectral problems related to a time dependent model in superconductivity with electric current (2009) (9)
On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern -- (2014) (8)
Improving Semigroup Bounds with Resolvent Estimates (2021) (8)
Thin domain limit and counterexamples to strong diamagnetism (2019) (8)
Periodic magnetic Schrödinger operators: Spectral gaps and tunneling effect (2008) (8)
The Semiclassical Regime for Ablation Front Models (2007) (8)
Decay of superconductivity away from the magnetic zero set (2016) (8)
Spectral theory for the dihedral group (2002) (7)
On Courant’s Nodal Domain Property for Linear Combinations of Eigenfunctions Part II (2017) (7)
Courant-sharp Robin eigenvalues for the square and other planar domains (2018) (7)
Magnetic calculus and semiclassical trace formulas (2010) (7)
Low lying spectral gaps induced by slowly varying magnetic fields (2016) (7)
On laplace integrals and transfer operators in large dimension: Examples in the nonconvex case (1996) (7)
Regularization of atomic Schrödinger operators with magnetic field (1995) (7)
Sturm's Theorem on the Zeros of Sums of Eigenfunctions: Gelfand's Strategy Implemented (2018) (7)
Superheating in a semi-infinite film in the weak $\kappa $ limit : numerical results and approximate models (1997) (6)
On the Domain of a Magnetic Schrödinger Operator with Complex Electric Potential (2017) (6)
On the Semiclassical Analysis of the Ground State Energy of the Dirichlet Pauli Operator in Non-Simply Connected Domains (2016) (6)
A Generalization of the Kustaanheimo–Stiefel Transform for Two–Centre Systems (1996) (6)
Positive Hausdorff Dimensional Spectrum for the Critical Almost Mathieu Operator (2018) (6)
On spectral minimal partitions: the disk revisited. (2013) (6)
Change of stability for symmetric bifurcating solutions in the Ginzburg–Landau equations (2000) (6)
Long Time Vanishing Property of Solutions of Sublinear Parabolic Equations and Semi-Classical Limit of Schrodinger Operators (2004) (6)
Spectral Minimal Partitions for a Thin Strip on a Cylinder or a Thin Annulus like Domain with Neumann Condition (2015) (6)
Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip (2020) (6)
Superheating field for the Ginzburg–Landau equations in the case of a large bounded interval (2000) (6)
Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit) (2021) (5)
Nodal domains in the disc---the Neumann case (2015) (5)
Tunneling effect induced by a curved magnetic edge (2022) (5)
Subelliptic estimates for some systems of complex vector fields: Quasihomogeneous case (2006) (5)
Comparison Between Different Notions of Resonances (1989) (5)
Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter (2019) (5)
On Schrödinger operators with magnetic fields (1988) (5)
Edited extracts from Antonie Stern’s thesis (2014) (5)
On the Stability of Laminar Flows Between Plates (2019) (4)
Non-boundedness of the number of nodal domains of a sum of eigenfunctions (2019) (4)
On the Subellipticity of Some Hypoelliptic Quasihomogeneous Systems of Complex Vector Fields (2010) (4)
PHASE TRANSITION IN THE SEMICLASSICAL REGIME (2000) (4)
On bifurcations from normal solutions for superconducting states (2000) (4)
On the nodal patterns of the 2D isotropic quantum harmonic oscillator (2015) (4)
On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator III: magnetic fields that change sign (2017) (4)
Periodic Schrödinger Operators and Aharonov—Bohm Hamiltonians (2003) (4)
Peierls' substitution for low lying spectral energy windows (2017) (4)
Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator (2001) (3)
Introduction to some conjectures for spectral minimal partitions (2011) (3)
Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains Application to the Extended Courant Property (2018) (3)
Semiclassical analysis of a nonlinear eigenvalue problem and nonanalytic hypoellipticity (2003) (3)
Semi-classical analysis for the transfer operator: WKB constructions in dimension 1 (1996) (3)
Lower bound for the number of critical points of minimal spectral k-partitions for k large (2015) (3)
A Priori Estimates for Ginzburg-Landau Solutions (2002) (3)
Spectral flow for pair compatible equipartitions (2020) (3)
Magnetic Confinement for the 3D Robin Laplacian (2020) (3)
From constant to non-degenerately vanishing magnetic fields in superconductivity (2015) (3)
The periodic magnetic Schr\"odinger operators: spectral gaps and tunneling effect (2007) (3)
Semi-classical Analysis for the Transfer Operator: Formal WKB Constructions in Large Dimension (1997) (3)
Laplace integrals and transfer operators (2002) (2)
Elliptic pseudo differential operators degenerate on a symplectic submanifold (1976) (2)
Some nodal properties of the quantum harmonic oscillator and other Schr{\"o}dinger operators in $\mathbb{R}^2$ (2015) (2)
The density of superconductivity in the bulk regime (2016) (2)
h-Pseudodifferential Operators and Applications (2006) (2)
Accurate Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator (2014) (2)
Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field (2020) (2)
Semi‐classical edge states for the Robin Laplacian (2021) (2)
Spectral Theory for Periodic Schrödinger Operators with Reflection Symmetries (2003) (2)
Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators (2017) (2)
On Schrödinger Equation in Large Dimension and Connected Problems in Statistical Mechanics (1993) (2)
Computing Nodal Deficiency with a Refined Dirichlet-to-Neumann Map (2022) (2)
Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon (2021) (2)
Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in R2 (2020) (2)
More counterexamples to the Extended Courant Property (ECP) (2018) (2)
Non-boundedness of the number of super level domains of eigenfunctions (2019) (2)
Analysis of the Bottom of the Spectrum of Schrödinger Operators with Magnetic Potentials and Applications (2005) (2)
ASYMPTOTICS FOR CRITICAL FIELDS IN AN APPROXIMATE GINZBURG–LANDAU MODEL IN THE LARGE SIZE LIMIT (1998) (1)
Spectral theory and applications. An elementary introductory course. Version 2008-2009 (2009) (1)
Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders (2020) (1)
Accurate estimates for magnetic bottles in connection with superconductivity (2004) (1)
An Euler-type formula for partitions of the M\"obius strip (2020) (1)
Superconductivity between HC 2 and HC 3 (2011) (1)
Quantum tunneling in deep potential wells and strong magnetic field revisited (2022) (1)
Global superheating field for superconductors in a large bounded interval (2002) (1)
Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter (2020) (1)
Maximal estimates for the Kramers-Fokker-Planck operator with electromagnetic field (2020) (1)
On Courant's Nodal Domain Property for Linear Combinations of Eigenfunctions. I (2018) (1)
ON THE CONTINUITY OF THE RESPONSE MAP AND AN ALTERNATIVE SHOOTING METHOD FOR THE HALF-SPACE GINZBURG–LANDAU MODEL (2006) (1)
On the spectrum of some Bloch–Torrey vector operators (2020) (1)
Stability estimates for semigroups in the Banach case (2023) (1)
On the spectral properties of the Bloch–Torrey equation in infinite periodically perforated domains (2020) (1)
On a Conjecture of P. Jorgensen and W.Klink (1987) (1)
On critical points of eigenvalues of the Montgomery family of quartic oscillators (2022) (1)
Discussing semigroup bounds with resolvent estimates (2023) (1)
Smoothness and analyticity for solutions of first order systems of partial differential equations on nilpotent Lie groups (1985) (1)
Study of interaction between the wells (1988) (0)
9. On Fokker-Planck Operators and Nilpotent Techniques (2005) (0)
UPPER CRITICAL FIELD AND LOCATION OF SURFACE NUCLEATION OF SUPERCONDUCTIVITY CHAMP SURCRITIQUE ET LOCALISATION DE LA NUCLÉATION DE SURFACE (2002) (0)
On magnetic wells in the semi-classical limit (2013) (0)
Spectral Theory and its Applications: Introduction (2013) (0)
The memoir ” Hofstadter butterfly revisited ” of Helffer-Kerdelhué-Sjöstrand revisited (2016) (0)
Spectral Theory and its Applications: Applications to non-self-adjoint one-dimensional models (2013) (0)
13. Decay of Eigenfunctions and Application to the Splitting (2005) (0)
Uniform decay of correlations (2002) (0)
On Other Models in Superconductivity and Open Problems (2009) (0)
Lower bound for the number of critical points of minimal spectral k-partitions for k large (2016) (0)
Spectral Analysis of Schrödinger Operators (2009) (0)
TUNNELING BETWEEN CORNERS FOR (2014) (0)
References and Index (2005) (0)
Compactness of the solution operator to d-bar in weighted L^2 - spaces (2006) (0)
1 COMPACTNESS OF THE SOLUTION OPERATOR TO ∂ IN (2006) (0)
Hypoellipticity, Spectral theory and Witten Laplacians (2003) (0)
2004 Nodal Domain Theorems `a la Courant. (2004) (0)
An introduction to recent results of Witten (1988) (0)
Between $$H_{C_2}$$ and $$H_{C_3}$$ in Two Dimensions (2009) (0)
Decay of superconductivity away from the magnetic zero set (2017) (0)
Four Lectures in Semiclassical Analysis for Non Self-Adjoint Problems with Applications to Hydrodynamic Instability (2008) (0)
The spectrum of a Schrödinger operator in a wire-like domain with a purely imaginary degenerate potential in the semiclassical limit (2018) (0)
On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator III: magnetic fields that change sign (2019) (0)
On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains – with some numerics – (2019) (0)
4. Global Pseudo-differential Calculus (2005) (0)
Log-Sobolev inequalities (2002) (0)
3. Compactness Criteria for the Resolvent of Schrödinger Operators (2005) (0)
Unbounded operators, adjoints, and self-adjoint operators (2012) (0)
Non-self-adjoint operators and pseudospectra (2012) (0)
ON THE ENERGY OF THE MINIMIZERS OF THE GINZBURG-LANDAU FUNCTIONAL FOR EXTERIOR MAGNETIC FIELDS BETWEEN HC2AND HC3 (2011) (0)
Periodic Schrödinger Operators with Constant Weak Magnetic Fields (1989) (0)
A problem of transversal anisotropic ellipticity A Problem of Transversal Anisotropic Ellipticity. (2021) (0)
Spectral theory for magnetic Schrodinger operators and applications (2008) (0)
Nodal Domain Theoremsla Courant. (2008) (0)
The Ginzburg–Landau Functional with Vanishing Magnetic Field (2015) (0)
Operators with Double Characteristics (2017) (0)
15. Semi-classical Analysis and Witten Laplacians: Tunneling Effects (2005) (0)
Superheating in a semi-infinite film in the weak κ limit : numerical results and approximatemodels RAIRO – (2009) (0)
Optimal Elliptic Estimates (2009) (0)
The density of superconductivity in domains with corners (2018) (0)
6. Return to Equilibrium for the Fokker-Planck Operator (2005) (0)
Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue (2022) (0)
7. Hypoellipticity and Nilpotent Groups (2005) (0)
5. Analysis of Some Fokker-Planck Operator (2005) (0)
Spectral Theory and its Applications: Applications to statistical mechanics and partial differential equations (2013) (0)
Generalities on semi-classical analysis (1988) (0)
8. Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts (2005) (0)
Spectral Theory and its Applications: Compact operators: general properties and examples (2013) (0)
Chambers’s Formula for the Graphene and the Hou Model with Kagome Periodicity and Applications (2015) (0)
Constant Field Models in Dimension 2: Discs and Their Complements (2009) (0)
Spectral Theory and its Applications: The max–min principle (2013) (0)
Applications in kinetic theory: the Fokker–Planck operator (2012) (0)
On Schrödinger operators with periodic electric potentials (1988) (0)
Basic facts in spectral theory and on the Schrödinger operator (2002) (0)
M ay 2 01 0 Magnetic calculus and semiclassical trace formulas (2021) (0)
Courant-sharp property for eigenfunctions of the Klein bottle (2020) (0)
12. Semi-classical Analysis for the Schrödinger Operator: Harmonic Approximation (2005) (0)
Spectral Theory and its Applications: Spectral questions about the Rayleigh equation (2013) (0)
Uniform log-Sobolev inequalities (2002) (0)
10. Maximal Microhypoellipticity for Systems and Applications to Witten Laplacians (2005) (0)
TUNNELING BETWEEN CORNERS FOR ROBIN LAPLACIANS BERNARD HELFFER (2017) (0)
Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications (2008) (0)
The Ginzburg–Landau Functional (2009) (0)
SEMI-CLASSICAL METHODS IN GINZBURG-LANDAU THEORY (2004) (0)
Spectral Theory and its Applications: Semibounded operators and the Friedrichs extension (2013) (0)
The discrete spectrum and essential spectrum (2012) (0)
11. Spectral Properties of the Witten-Laplacians in Connection with Poincaré Inequalities for Laplace Integrals (2005) (0)
Upper bounds on eigenvalue multiplicities for surfaces of genus $0$ revisited (Work in progress) (2022) (0)
Problems in statistical mechanics with discrete spins (2002) (0)
Talenti’s comparison theorem revisited (2018) (0)
Remarks on Floquet eigenvalues in the semi-classical regime (2004) (0)
Witten Laplacians approach (2002) (0)
On maximal multiplicities for Hamiltonians with separable variables (2019) (0)
Models in Dimension 3: $\mathbb{R}^3$ or $\mathbb{R}^{3,+}$ (2009) (0)
Pleijel’s theorem for Schrödinger operators with radial potentials (2017) (0)
Positive Hausdorff Dimensional Spectrum for the Critical Almost Mathieu Operator (2018) (0)
Constant Field Models in Dimension 2: Noncompact Case (2009) (0)
On the Semiclassical Analysis of the Ground State Energy of the Dirichlet Pauli Operator in Non-Simply Connected Domains (2017) (0)
Inequalities for the lowest magnetic Neumann eigenvalue (2019) (0)
SP ] 5 A pr 2 01 7 Low lying spectral gaps induced by slowly varying magnetic fields April 5 , 2017 (2017) (0)
Models in One Dimension (2009) (0)
Low Lying Eigenvalues of Witten Laplacians and Metastability (After Hel.er-Klein-Nier and Helffer-Nier) (2006) (0)
Semi-classical analysis for the transfer operators (2002) (0)
Mixed Normal-Superconducting States in the Presence of Strong Electric Currents (2016) (0)
Spectral Theory and its Applications: Essentially self-adjoint operators (2013) (0)
17. Application to the Fokker-Planck Equation (2005) (0)
Global Stability of the Normal State of Superconductors in the Presence of a Strong Electric Current (2014) (0)
On non self-adjoint spectral problems occurring in superconductivity (2015) (0)
On the Third Critical Field H_{C_3} (2009) (0)
Courant-Sharp Eigenvalues for the Equilateral Torus, and for the Equilateral Triangle (2016) (0)
Tunneling effect for Witten Laplacians and Kramers operators ( After Helffer-Klein-Nier , Helffer-Nier and Hérau-Hitrik-Sjöstrand ) (2007) (0)
Spectral Theory and its Applications: Self-adjoint unbounded operators and spectral theory (2013) (0)
Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter (2019) (0)
Large Field Asymptotics of the Magnetic Schrödinger Operator: The Case of Dimension 2 (2009) (0)
B.K.W. Construction for a potential near the bottom in the case of non-degenerate minima (1988) (0)
On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains (2020) (0)
Main Results for Large Magnetic Fields in Dimension 3 (2009) (0)
ETS volume 33 issue 4 Cover and Back matter (2013) (0)
A. Stern’s analysis of the nodal sets of some families of spherical harmonics revisited (2015) (0)
2 Lecture 1 : The Rayleigh – Taylor Model 2 . 1 The Rayleigh – Taylor Model : (2008) (0)
The decay of the eigenfunctions (1988) (0)
16. Accurate Asymptotics for the Exponentially Small Eigenvalues of \Delta_{f,h}^{(0)} (2005) (0)
Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames (2022) (0)
WITH NON-VANISHING MAGNETIC FIELD (2013) (0)
Improving Semigroup Bounds with Resolvent Estimates (2021) (0)
Introduction to Semiclassical Methods for the Schrödinger Operator with a Large Electric Potential (2009) (0)
Nodal domains a la Courant (2004) (0)
Effective operators on an attractive magnetic edge (2022) (0)
On the time dependent Ginzburg-Landau system (2013) (0)
14. Semi-classical Analysis and Witten Laplacians: Morse Inequalities (2005) (0)
A ug 2 01 1 Sharp trace asymptotics for a class of 2 D-magnetic operators July 29 , 2011 (2011) (0)
C V ] 3 J ul 2 00 6 COMPACTNESS OF THE SOLUTION OPERATOR TO ∂ IN WEIGHTED L 2-SPACES (2019) (0)
Spectral theory for bounded operators (2012) (0)
2. Kohn’s Proof of the Hypoellipticity of the Hörmander Operators (2005) (0)
On the Problems with Corners (2009) (0)
On spectral minimal partitions II, the case of the rectangle (2008) (0)
On the stability of symmetric flows in a two-dimensional channel (2022) (0)

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