Haïm Brezis

Q: What Schools Are Affiliated With Haïm Brezis

Haïm Brezis is affiliated with the following schools: Rutgers University, Technion – Israel Institute of Technology, Sorbonne University

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Haïm Brezis

Mathematics

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#462

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Functional Analysis

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Measure Theory

#144

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#226

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Why Is Haïm Brezis Influential?

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According to Wikipedia, Haïm Brezis is a French mathematician, who mainly works in functional analysis and partial differential equations. Biography Born in Riom-ès-Montagnes, Cantal, France. Brezis is the son of a Romanian immigrant father, who came to France in the 1930s, and a Jewish mother who fled from the Netherlands. His wife, Michal Govrin, a native Israeli, works as a novelist, poet, and theater director. Brezis received his Ph.D. from the University of Paris in 1972 under the supervision of Gustave Choquet. He is currently a professor at the Pierre and Marie Curie University and a visiting distinguished professor at Rutgers University. He is a member of the Academia Europaea and a foreign associate of the United States National Academy of Sciences . In 2012 he became a fellow of the American Mathematical Society. He holds honorary doctorates from several universities including National Technical University of Athens. Brezis is listed as an ISI highly cited researcher. He also served on the Mathematical Sciences jury for the Infosys Prize in 2013 and 2014.

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Haïm Brezis'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

Functional Analysis, Sobolev Spaces and Partial Differential Equations (2010) (4568)
Positive solutions of nonlinear elliptic equations involving critical sobolev exponents (1983) (2611)
A Relation Between Pointwise Convergence of Functions and Convergence of Functionals (1983) (1972)
Analyse fonctionnelle : théorie et applications (1983) (1969)
Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems (1994) (1087)
Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)eu in two dimensions (1991) (709)
Blow-up solutions of some nonlinear elliptic problems (1997) (592)
Another look at Sobolev spaces (2001) (513)
Nonlinear Schrödinger evolution equations (1980) (503)
A note on limiting cases of sobolev embeddings and convolution inequalities (1980) (502)
Semi-linear second-order elliptic equations in L 1 (1973) (498)
Remarks on sublinear elliptic equations (1986) (439)
Monotonicity Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations (1971) (428)
Remarks on finding critical points (1991) (401)
Hardy's inequalities revisited (1997) (340)
Remarks on the Euler equation (1974) (333)
Sublinear elliptic equations in ℝn (1992) (330)
Asymptotics for the minimization of a Ginzburg-Landau functional (1993) (321)
Convergence of solutions of H-systems or how to blow bubbles (1985) (309)
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems (1978) (306)
H1 versus C1 local minimizers (1993) (285)
Nonlinear Parabolic Equations Involving Measures as Initial Conditions (1981) (284)
Some simple nonlinear PDE's without solutions (1998) (256)
Degree theory and BMO; part I: Compact manifolds without boundaries (1995) (249)
Multiple solutions of H‐systems and Rellich's conjecture (1984) (236)
Perturbations of nonlinear maximal monotone sets in banach space (1970) (231)
Removable singularities for some nonlinear elliptic equations (1980) (216)
Convergence and approximation of semigroups of nonlinear operators in Banach spaces (1972) (214)
A general principle on ordered sets in nonlinear functional analysis (1976) (213)
Duality for the Sum of Convex Functions in General Banach Spaces (1986) (208)
On a class of superlinear elliptic problems (1977) (208)
Periodic solutions of nonlinear vibrating strings and duality principles (1983) (202)
Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces (2001) (202)
The Thomas—Fermi—von Weizsäcker Theory of Atoms and Molecules (1981) (201)
Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz (1980) (200)
Lifting in Sobolev spaces (2000) (194)
Asymptotics for Elliptic Equations Involving Critical Growth (1989) (182)
How to recognize constant functions. Connections with Sobolev spaces (2002) (181)
Blow up for $u_t-\Delta u=g(u)$ revisited (1996) (177)
Minimum action solutions of some vector field equations (1984) (169)
A remark on Ky fan's minimax principle (2008) (167)
Sobolev inequalities with remainder terms (1985) (164)
On a characterization of flow-invariant sets (1970) (159)
On the equation DIV Y = f and applications to control of phases (2002) (156)
Nonlinear problems related to the Thomas-Fermi equation (2003) (148)
Large solutions for harmonic maps in two dimensions (1983) (144)
The Smoothness of Solutions to Nonlinear Variational Inequalities (1974) (140)
New estimates for elliptic equations and Hodge type systems (2007) (136)
Relaxed Energies for Harmonic Maps (1990) (123)
Asymptotics for the Ginzburg–Landau Equation in Arbitrary Dimensions (2001) (121)
A sup + inf Inequality for Some Nonlinear Elliptic Equations Involving Exponential Nonlinearities (1993) (121)
A semilinear equation in $L^1 (\mathbb {R}^N)$ (1975) (120)
H1/2 maps with values into the circle: Minimal Connections, Lifting, and the Ginzburg–Landau equation (2004) (120)
On the equation = and application to control of phases (2002) (117)
Nonlinear elliptic equations with measures revisited (2007) (115)
On a free boundary problem arising in plasma physics (1980) (114)
Quantization effects for −Δu = u(1 − |u|2) in ℝ2 (1994) (109)
Nonlinear integral equations and systems of Hammerstein type (1975) (107)
New estimates for the Laplacian, the div-curl, and related Hodge systems (2004) (106)
Semigroups of nonlinear contractions on convex sets (1970) (105)
Remarks on the preceding paper by M. Ben-Artzi “Global solutions of two-dimensional Navier-Stokes and Euler equations” (1994) (104)
Extremal Functions for Hardy's Inequality with Weight (2000) (99)
Equivalence de deux inéquations variationnelles et applications (1971) (95)
Nodal solutions of elliptic equations with critical Sobolev exponents (1990) (95)
Semilinear Equations in RN without conditions at infinity (1983) (94)
Existence theorems for nonlinear integral equations of Hammerstein type (1975) (84)
Elliptic equations with limiting sobolev exponents—the impact of topology (1986) (81)
A numerical method for solving the problem $u_t - \Delta f (u) = 0$ (1979) (78)
On a semilinear elliptic equation with inverse-square potential (2005) (76)
Accretive sets and differential equations in Banach spaces (1970) (74)
On the Optimality of Shape and Data Representation in the Spectral Domain (2014) (74)
Estimates on the support of solutions of parabolic variational inequalities (1976) (71)
Some new results about Hammerstein equations (1974) (70)
Kato's inequality when Δu is a measure (2004) (68)
Multiplicateur de lagrange en torsion elasto-plastique (1972) (67)
Forced vibrations for a nonlinear wave equation (2010) (65)
Topology and Sobolev Spaces (2000) (64)
Nonlinear ergodic theorems (1976) (63)
The Jacobian determinant revisited (2011) (60)
Remarks on the strong maximum principle (2003) (59)
On the structure of the Sobolev space H1/2 with values into the circle (2000) (58)
Nonlinear partial differential equations and their applications : Collège de France seminar (1982) (58)
Periodic solutions of a nonlinear wave equation (1980) (58)
The Thomas-Fermi-von Weizsäcker theory of atoms and molecules (1981) (56)
Bifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders (1992) (55)
Non-linear elliptic equations on Riemannian manifolds with the Sobolev critical exponent (1996) (55)
Strongly nonlinear elliptic boundary value problems (1978) (54)
Lifting, degree, and distributional Jacobian revisited (2005) (54)
Integrability for the Jacobian of orientation preserving mappings (1993) (51)
Asymptotic Behavior of Some Evolution Systems (1978) (48)
Singular solutions for some semilinear elliptic equations (1987) (48)
Boundary estimates for elliptic systems with L1–data (2000) (48)
Some remarks on a class of elliptic equations with degenerate coercivity (2003) (47)
The interplay between analysis and topology in some nonlinear PDE problems (2003) (46)
A property of sobolev spaces (1979) (46)
SOLUTIONS WITH COMPACT SUPPORT OF VARIATIONAL INEQUALITIES (1974) (46)
Long range atomic potentials in Thomas-Fermi theory (1979) (46)
Remarks on nonlinear ergodic theory (1977) (45)
Nonlinear Elliptic Equations Involving the Critical Sobolev Exponent—Survey and Perspectives (1987) (45)
Reinforcement problems for elliptic equations and variational inequalities (1980) (43)
A variational inequality approach to the Bellman-Dirichlet equation for two elliptic operators (1977) (43)
New Questions Related to the Topological Degree (2006) (42)
Periodic Solutions of Nonlinear Wave Equations and Hamiltonian Systems (1981) (42)
Equations d’evolution du second ordre associees a des operateurs monotones (1972) (42)
On a degenerate elliptic‐parabolic equation occurring in the theory of probability (1971) (40)
Degree and Sobolev spaces (1999) (39)
A new function space and applications (2015) (38)
Elliptic equations with critical exponent on spherical caps of S3 (2006) (36)
Jensen's inequality in the calculus of variations (1994) (36)
A semilinear elliptic equation in L[1] (IR[n]) (1975) (36)
The BBM formula revisited (2016) (32)
On Harnack's inequality for a class of strongly degenerate Schrödinger operators formed by vector fields (1994) (32)
BMO‐Type Norms Related to the Perimeter of Sets (2014) (31)
Sk—Valued maps with singularities (1989) (31)
W^{1,1}-maps with values into S^1 (2004) (30)
Liquid Crystals and Energy Estimates for S2-Valued Maps (1987) (30)
Linear Maximal Monotone Operators and Singular Nonlinear Integral Equations of Hammerstein Type (1978) (29)
Reduced measures on the boundary (2005) (29)
Two subtle convex nonlocal approximations of the BV-norm (2016) (29)
Kato's Inequality Up To the Boundary (2008) (28)
A surprising formula for Sobolev norms (2020) (28)
A new estimate for the topological degree (2005) (28)
Degree Theory: Old and New (1997) (28)
New approximations of the total variation and filters in Imaging (2015) (27)
Removable singularities for nonlinear elliptic equations (1997) (27)
On a conjecture of J. Serrin (2008) (26)
Reduced measures for obstacle problems (2005) (25)
Remarks on the Monge–Kantorovich problem in the discrete setting (2018) (25)
A VARIATIONAL FORMULATION FOR THE TWO-SIDED OBSTACLE PROBLEM WITH MEASURE DATA (2002) (24)
Small energy solutions to the Ginzburg-Landau equation (2000) (24)
Regularity of minimizers of relaxed problems for harmonic maps (1991) (24)
Remarks on some fourth order variational inequalities (1977) (23)
A numerical method for solving the problem u t - Δ f ( u ) = 0 (2009) (23)
The hodograph method in fluid-dynamics in the light of variational inequalities (1976) (22)
On the distributional Jacobian of maps from SN into SN in fractional Sobolev and Holder spaces (2011) (22)
Periodic solutions of lagrangian systems of relativistic oscillators (2011) (21)
Methodes d'approximation et d'iteration pour les Operateurs Monotones (2010) (21)
A new concept of reduced measure for nonlinear elliptic equations (2004) (21)
Semigroups, theory and applications (1986) (20)
On a new class of functions related to VMO (2011) (20)
New Results Concerning Monotone Operators and Nonlinear Semigroups (非線形問題の解析 : Analysis of Nonlinear Problems, RIMS, 1974) (1975) (19)
On a problem of T. Kato (1971) (18)
Some first‐order nonlinear equations on a torus (1977) (17)
On some questions of topology for S1-valued fractional Sobolev spaces (2001) (17)
Composition in fractional Sobolev spaces (2001) (17)
Elliptic equations with critical exponent on S3: new non-minimising solutions (2004) (16)
Comments on two Notes by L. Ma and X. Xu (2011) (16)
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail (2021) (16)
Circulation integrals and critical Sobolev spaces: problems of optimal constants (2008) (15)
Review: David Kinderlehrer and Guido Stampacchia, An introduction to variational inequalities and their applications (1982) (15)
Estimates on the Free Boundary for Quasi Variational Inequalities (1977) (15)
W1,p estimates for solutions to the Ginzburg–Landau equation with boundary data in H1/2 (2001) (14)
Maximal monotone operators in nonreflexive Banach spaces and nonlinear integral equations of Hammerstein type (1975) (14)
Noncompact problems at the intersection of geometry, analysis, and topology : proceedings of the Brezis-Browder Conference, Noncompact Variational Problems and General Relativity, October 14-18, 2001, Rutgers, the State University of New Jersey, New Brunswick, NJ (2004) (14)
Strongly nonlinear parabolic variational inequalities. (1980) (13)
Singular Hammerstein equations and maximal monotone operators (1976) (13)
Complements to the paper "Lifting, degree, and the Distributional Jacobian Revisited" (2004) (12)
Best bases for signal spaces (2016) (12)
An extension of Khintchine's estimate for large deviations to a class of Markov chains converging to a singular diffusion (1971) (12)
Nonlinear Elliptic and Parabolic Problems (2005) (12)
Non-local, non-convex functionals converging to Sobolev norms (2019) (12)
Nonlinear Schroedinger Evolution Equations. (1979) (11)
Non-convex, non-local functionals converging to the total variation (2017) (11)
Density in W s , p ( Ω ; N ) (2015) (11)
A Incompressible ﬂows of an ideal ﬂuid with vorticity in borderline spaces of Besov type (2018) (11)
Maximum principles for integro-differential parabolic operators (1995) (11)
Recent contributions to nonlinear partial differential equations (1981) (10)
W^{1,p} estimates for solutions to the Ginzburg-Landau equation with boundary data in H^{1/2}. (2001) (10)
Journal of Convex Analysis (2012) (10)
Metastable Harmonic Maps (1987) (9)
Chapter 4. Nonlinear Elliptic Equations with Measures Revisited (2009) (9)
New questions related to the topological degree. The unity of mathematics (2006) (9)
Elliptic and parabolic problems : a special tribute to the work of Haim Brezis (2005) (9)
On some nonlinear equations with critical exponents (2008) (9)
LOCAL REGULARITY RESULTS FOR SOME PARABOLIC EQUATIONS (1999) (8)
Partial differential equations and mathematical physics (1996) (8)
Initiation of subsonic detonation (2000) (7)
SOME REMARKS ON LIOUVILLE TYPE THEOREMS (2008) (7)
Analysis and Continuum Mechanics: A Collection of Papers Dedicated to J. Serrin on His Sixtieth Birthday (1989) (7)
Complements to the paper ”W1,1-maps with values into S1” (2016) (7)
The Plateau problem from the perspective of optimal transport (2019) (7)
Perimeter of sets and BMO-type norms (2014) (7)
Nonlinear Evolution Equations and Related Topics (2004) (6)
Density in Ws,p(Ω;N) (2015) (6)
Rigidity of optimal bases for signal spaces (2017) (6)
Interpolation classes for monotone operators (1975) (6)
New energies for harmonic maps and liquid crystals (1993) (6)
The fascinating homotopy structure of sobolev spaces (2003) (5)
Nonlinear Ergodic Theorems for Asymptotically Nonexpansive Mappings in Banach Spaces Satisfying Opial’s Condition (2003) (5)
Non linear perturbations of monotone operators (1972) (5)
A new method in the study of subsonic flows (1975) (5)
Analysis and Continuum Mechanics (1989) (5)
A function with prescribed initial derivatives in different Banach spaces (1978) (5)
A surprising formula for Sobolev norms and related topics (2020) (5)
Distances between homotopy classes of Ws,p(N;N) (2016) (5)
Energy with Weight for S 2-Valued Maps with Prescribed Singularities (2004) (5)
A Semilinear Elliptic Equation in (L sup 1)(R sup N). (1975) (4)
Erratum: "Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions," (Journal of Functional Analysis (2001) vol. 186 (2) (432-520)) (2002) (4)
Distances between classes of sphere-valued Sobolev maps (2016) (4)
Distances between classes in W 1 ; 1 (Ω; S 1 ) (2017) (4)
Remarks on some minimization problems associated with BV norms (2019) (3)
On some questions of topology for ${\mathbb S}^1$-valued fractional Sobolev spaces (2001) (3)
Sobolev spaces revisited (2022) (3)
Distances between classes in $$W^{1,1}(\Omega ;{\mathbb {S}}^{1})$$W1,1(Ω;S1) (2016) (3)
On the Range of the sum of Nonlinear Operators (1976) (3)
BIow-up solutions of sorne nonhinear elliptic problems. (1997) (3)
Γ-convergence of non-local, non-convex functionals in one dimension (2019) (3)
Morse theory, minimax theory and their applications to nonlinear differential equations : held at Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing April 1st to September 30th, 1999 (2003) (2)
Solutions à support compact d'inéquations variationnelles (1974) (2)
L p Spaces (2011) (1)
Nonlinear Evolution Equations and Related Topics: Dedicated to Philippe Bénilan (2005) (1)
Mathematical Problems Related to Liquid Crystals, Superconductors and Superfluids (1994) (1)
Remarks on Sublinear Equations (1984) (1)
" W ^ { 1 , 1 }-maps with values into S ^ 1 " (2019) (1)
maps with values into $S^1$, (2005) (1)
Energy estimates for S1-valued maps (1994) (1)
Mathematical problems of liquid crystals (1990) (1)
New developments on the Ginzburg-Landau model (1994) (1)
Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension (2011) (1)
Kato's inequality when $\Delta u$ is a measure (2013) (1)
Singular perturbations of hyperbolic systems (1974) (1)
Families of functionals representing Sobolev norms (2021) (1)
A finite difference scheme in Hilbert spaces (2003) (1)
Sobolev Maps to the Circle (2021) (1)
Homotopy classes in Sobolev spaces (1)
Some additional properties of UE (1994) (0)
The hypothesis N ≥ 7 in Theorem 1 . 2 is necessary for the existence of radial nodal solutions by a result of (2000) (0)
Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity (2011) (0)
Distances between classes in W1,1(Ω;S1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W^{1,1}(\Omega ;{\mathbb {S}}^{ (2017) (0)
The Hamilton-Jacobi-Bellman Equation for Two Operators Via Variational Inequalities (1978) (0)
Partial differential equations / Theory of signals Rigidity of optimal bases for signal spaces Rigidité des bases optimales pour les espaces de signaux (2017) (0)
Louis Nirenberg (1925–2020) (2021) (0)
Some basic estimateds for UE (2017) (0)
Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators (2011) (0)
The Uniform Boundedness Principle and the Closed Graph Theorem (2011) (0)
A brief history of the Jacobian (2023) (0)
An upper bound for the energy of u∈ away from the singularities (1994) (0)
The geometry of Ju and $$\varSigma (u)$$ in 2D; point singularities and minimal connections (2021) (0)
Estimates of phases: positive and negative results (2021) (0)
The geometry of Ju and $$\varSigma (u)$$ in 3D (and higher); line singularities and minimal surfaces (2021) (0)
A digression: sphere-valued maps (2021) (0)
Vesna Županović, full professor, FER, University of Zagreb, Croatia (2015) (0)
Dirichlet problems. Gaps. Infinite energies (2021) (0)
Radial extensions in fractional Sobolev spaces (2018) (0)
The Hille–Yosida Theorem (2011) (0)
Applications of the factorization (2021) (0)
u ★ coincides with THE canonical harmonic map having singularities ( a j ) (1994) (0)
The configuration (aj) minimizes the renormalized energy W (1994) (0)
Complements to the paper "$W^{1,1}$-maps with values into ${\mathbb S}^1$" (2004) (0)
On the convexity of the level lines of certain solutions of a class of semilinear equations with non monotone non-linearity (1989) (0)
UEn Converges:U* is born! (1994) (0)
Strongly nonlinear parabolic initial-boundary value problems ( Dirichlet boundary conditions / compactness theorems / approximation theorems with convex side conditions ) (0)
Felix Browder (1927-2016) (2018) (0)
Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions (2011) (0)
I.14. Pathological Solutions (2014) (0)
VII.1 Surfaces of Constant Mean Curvature (2014) (0)
A sharp relative isoperimetric inequality for the square (2021) (0)
Density in $W^{s,p}(\Omega ; N)$ (2015) (0)
Towards locating the singularties: bad discs and good discs (1994) (0)
Paul Malliavin and the Journal of Functional Analysis (2008) (0)
Radial extensions in fractional Sobolev spaces (2018) (0)
Uniqueness of lifting and beyond (2021) (0)
Topological methods, variational methods and their applications : ICM 2002 Satellite Conference on Nonlinear Functinal Analysis : Taiyuan, Shan Xi, P.R. China, August 14-18, 2002 (2003) (0)
HAÏM BREZIS THE FASCINATING HOMOTOPY STRUCTURE OF SOBOLEV SPACES (2004) (0)
Lifttng I-n Sobolev Spaces (2007) (0)
A global solution curve for a class of free boundary value problems arising in plasma physics (0)
Lifting in fractional Sobolev spaces and in $$\textit{VMO}\, $$ (2021) (0)
ON THE STRUCTURE OF SOLUTIONS OF A CLASS OF BOUNDARY VALUE PROBLEMS (1999) (0)
ACCRETIVE SETS A N D DIFFERENTIAL EQUATIONS IN BANACH SPACES (2007) (0)
Applications of Mathematics E. G. Ladopoulos; V. A. Zisis Existence and uniqueness for non-linear singular integral equations used in fluid mechanics (2020) (0)
First Order Quasilinear Equations on a Torus (2011) (0)
Variational Problems Involving Lack of Compactness and Rellich's Conjecture (1984) (0)
Non-minimizing solutions of the Ginzburg-Landau equation (1994) (0)
Introduction. Dedicated to Philippe Bénilan (2003) (0)
Non Linear Evolution Equations of Schrodinger Type (1980) (0)
Partial Di¤erential Equations — A failing in the Calderon-Zygmund theory of Dirichlet problems for linear equations with discontinuous coe‰cients, by Lucio (2015) (0)
Effects de quantification pour -Δu=u(1-|u|2) sur R2 (1993) (0)
Domains with topology (2021) (0)
Non-local Functionals Related to the Total Variation and Connections with Image Processing (2018) (0)
Energy estimates for surface-valued maps with prescribed singularities (1989) (0)
The lower bound for the energy of S-valued maps on Perforated domains (1994) (0)
Chapter Four Nonlinear Elliptic Equations with Measures Revisited (0)
Symposium on Partial Differential Equations to celebrate the Seventy-Fifth Birthday of James Serrin (2002) (0)
The Hahn–Banach Theorems. Introduction to the Theory of Conjugate Convex Functions (2011) (0)
Some basic estimates for u (1994) (0)
Evolution Problems: The Heat Equation and the Wave Equation (2011) (0)
Going to weak $L^p$ when fractional Sobolev, Gagliardo and Nirenberg estimates fail (2020) (0)
Mathematical analysis / Theory of signals Best bases for signal spaces Bases optimales pour des espaces de signaux (2016) (0)
Lifting in $$W^{1,p}$$ (2021) (0)
Mathematical analysis / Partial differential equations Non-convex , non-local functionals converging to the total variation Convergence de fonctionnelles non convexes et non locales vers la variation totale (2016) (0)
Minimizers of the W 1 , 1-energy of S 1-valued maps with prescribed singularities . Do they exist ? (2018) (0)
Nonlinear Equations of the Thomas-Fermi Type (Nonlinear Functional Analysis) (1981) (0)
A maximization problem involving critical Sobolev exponents (1987) (0)

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What Schools Are Affiliated With Haïm Brezis?

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