Bernard Dacorogna | Academic Influence

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Bernard Dacorogna

Mathematics

#1240

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#2078

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Measure Theory

#1143

World Rank

#1463

Historical Rank

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Mathematics

Bernard Dacorogna's Degrees

PhD Mathematics University of Geneva

Why Is Bernard Dacorogna Influential?

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According to Wikipedia, Bernard Dacorogna is a Swiss mathematician, born 15 October 1953, in Alexandria, Egypt. He completed his undergraduate studies at the University of Geneva in Switzerland and his Ph.D. at Heriot-Watt University in Edinburgh, UK, in 1980 under the supervision of John M. Ball. He is professor at Ecole Polytechnique Fédérale de Lausanne , Switzerland. He is a specialist of the calculus of variations and of partial differential equations. He has written several articles and books. The Chaire de la Vallée Poussin 2018 of the Université Catholique de Louvain is attributed to him.

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Bernard Dacorogna'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

Direct methods in the calculus of variations (1989) (1577)
On a partial differential equation involving the Jacobian determinant (1990) (366)
Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals (1982) (342)
Implicit partial differential equations (1999) (216)
Quasiconvexity and relaxation of nonconvex problems in the calculus of variations (1982) (162)
Optimal Foraging on Arbitrary Food Distributions and the Definition of Habitat Patches (1988) (162)
General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases (1997) (155)
Introduction to the calculus of variations (2004) (116)
The Pullback Equation for Differential Forms (2011) (103)
An example of a quasiconvex function that is not polyconvex in two dimensions (1992) (73)
Wulff theorem and best constant in Sobolev inequality (1992) (72)
Sur une généralisation de l’inégalité de Wirtinger (1992) (60)
Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension (2001) (58)
A relaxation theorem and its application to the equilibrium of gases (1981) (56)
Calculus of Variations and Nonlinear Partial Differential Equations (2007) (46)
Cauchy-Dirichlet problem for first order nonlinear systems. (Sur le problème de Cauchy-Dirichlet pour les systèmes d' équationsnon linéaires du premier ordre.) (1998) (45)
Semicontinuité pour des intégrandes polyconvexes sans continuité des déterminants (1990) (44)
The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity (2008) (43)
Existence of minimizers for non-quasiconvex integrals (1995) (43)
An existence theorem for slightly compressible materials in nonlinear elasticity (1988) (40)
On a generalized Wirtinger inequality (2003) (36)
Manifold constrained variational problems (1999) (35)
A-B quasiconvexity and implicit partial differential equations (2002) (35)
Théorèmes d" existence dans les cas scalaire et vectoriel pour les équations de Hamilton-Jacobi (1996) (34)
Some examples of rank one convex functions in dimension two (1990) (31)
Lipschitz-continuous local isometric immersions: rigid maps and origami (2008) (31)
On the different notions of convexity for rotationally invariant functions (1993) (30)
A GENERAL EXISTENCE THEOREM FOR DIFFERENTIAL INCLUSIONS IN THE VECTOR VALUED CASE (2005) (27)
Implicit partial differential equations and the constraints of nonlinear elasticity (2002) (25)
On non quasiconvex problems of the calculus of variations (2005) (23)
Geometric restrictions for the existence of viscosity solutions (1999) (22)
On the optimality of certain Sobolev exponents for the weak continuity of determinants (1992) (22)
Introduction au calcul des variations (1992) (22)
Sur le problème de Cauchy-Dirichlet pour les systèmes d'équations non linéaires du premier ordre (1996) (22)
Existence and Regularity of Solutions of dω = f with Dirichlet Boundary Conditions (2002) (21)
On the different convex hulls of sets involving singular values (1998) (19)
Some numerical methods for the study of the convexity notions arising in the calculus of variations (1998) (17)
Optimal foraging in nonpatchy habitats. I. Bounded one-dimensional resource. (1985) (16)
Existence of solutions for some implicit partial differential equations and applications to variational integrals involving quasi-affine functions (2004) (16)
On the solvability of the equation div $u = f$ in $L^{1}$ and in $C^{0}$ (2003) (16)
On the envelopes of functions depending on singular values of matrices (1994) (16)
Calculus of variations with differential forms (2015) (15)
Optimal transport of closed differential forms for convex costs (2015) (15)
Numerical methods for the solution of a system of Eikonal equations with Dirichlet boundary conditions (2003) (15)
An explicit solution to a system of implicit differential equations (2008) (15)
Remarques sur les notions de polyconvexité, quasi-convexité et convexité de rang 1. (Remarks on polyconvexity, quasi-convexityand rank 1 convexity). (1985) (15)
Extension theorems for vector valued maps (2006) (15)
On the pullback equation φ*(g)=f (2009) (14)
On some definitions and properties of generalized convex sets arising in the calculus of variations (2006) (12)
Minima absolus pour des énergies ferromagnétiques (2000) (12)
On the equation $${{\rm det}\,\nabla{u}=f}$$ with no sign hypothesis (2009) (12)
Existence and non-existence results for non-coercive variational problems and applications in ecology (1990) (12)
Differential inclusions for differential forms (2007) (12)
On a Conjugate Gradient/Newton/Penalty Method for the Solution of Obstacle Problems. Application to the Solution of an Eikonal System with Dirichlet Boundary Conditions (2004) (11)
Symplectic factorization, Darboux theorem and ellipticity (2017) (11)
A minimization problem involving variation of the domain (1992) (11)
Non convex problems of the calculus of variations and differential inclusions (2005) (11)
Existence of solutions for a variational problem associated to models in optimal foraging theory (1990) (10)
On the n-dimensional Dirichlet problem for isometric maps (2008) (10)
An identity involving exterior derivatives and applications to Gaffney inequality (2011) (9)
On the best constant in Gaffney inequality (2017) (9)
Integral Convexity and Parabolic Systems (2020) (9)
Viscosity solutions, almost everywhere solutions and explicit formulas (2004) (9)
Convex SO ( N ) × SO ( n )-invariant Functions and Refinements of Von Neumann ’ s Inequality (2005) (9)
Calculus of Variations On the equation det ∇ u = f with no sign hypothesis (2009) (8)
Minimal hypersurfaces problems in parametric form with nonconvex integrands (1982) (8)
Quasi-convexité et semi-continuité inférieure faible des fonctionnelles non linéaires (1982) (8)
SMOOTH CONJUGACY AND LINEARIZATION NEAR RESONANT FIXED POINTS IN HILBERT SPACES (2014) (8)
The Pullback Equation For Degenerate Forms (2010) (8)
Optimal foraging in nonpatchy habitats. 2: Unbounded one-dimensional habitat (1987) (8)
Convexity of certain integrals of the calculus of variations—II (1990) (7)
Transportation of closed differential forms with non-homogeneous convex costs (2018) (7)
Attainment of minima and implicit partial differential equations (1999) (7)
Functions with orthogonal Hessian (2010) (7)
A characterization of pseudo-monotone differential operators in divergence form (1984) (7)
Convex $\operatorname{SO}(N)\times \operatorname{SO}(n)$-invariant functions and refinements of von Neumann’s inequality (2007) (7)
Semi-continuité des fonctionnelles avec contraintes du type "det $\nabla u>0$" (1985) (7)
Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère (2012) (7)
On convexity properties of homogeneous functions of degree one (1996) (7)
Implicit second order partial differential equations (1997) (6)
Qualitative properties of Lipschitz solutions of eikonal type systems (2006) (6)
A note on spectrally defined polyconvex functions (2006) (6)
Remarks on a Numerical Study of Convexity, Quasiconvexity, and Rank One Convexity (1996) (5)
Maximum sustainable yield of populations with continuous age-structure. (1992) (5)
A Dirichlet problem involving the divergence operator (2016) (4)
Maximum sustainable yield with continuous age structure and density-dependent recruitment. (1994) (4)
Monotonicity of certain differential operators in divergence form (1989) (4)
Équations de type implicite avec contraintes (2000) (4)
Divisibility in Grassmann algebra (2011) (4)
The second order pullback equation (2014) (4)
A global version of the Darboux theorem with optimal regularity and Dirichlet condition (2011) (4)
Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms (2019) (4)
Vector-Valued Partial Differential Equations and Applications (2017) (3)
Semicontinuité pour des intégrandes polyconvexes sans continuitédes déterminants. (Semicontinuity for polyconvex integrands withoutcontinuity of determinants). (1990) (3)
Regularity and selecting principles for implicit ordinary differential equations (2008) (3)
First-Order Elliptic Systems of Cauchy–Riemann Type (2012) (3)
Some New Results On Differential Inclusions For Differential Forms (2014) (3)
The two well problem for piecewise affine maps (2012) (2)
Optimal Foraging in Nonpatchy Habitats (2001) (2)
Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms (2017) (2)
Coercivity of integrals versus coercivity of integrands (1995) (2)
The degenerate two well problem for piecewise affine maps (2013) (2)
Some Geometrical and Algebraic Properties of Various Types of Convex Hulls (2006) (2)
On the solvability of implicit nonlinear systems in the vectorial case (2013) (2)
The Vectorial Case (1989) (1)
Regularization of Non Elliptic Variational Problems (1983) (1)
Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form (2021) (1)
Calcul des variations (2007) (1)
FA ] 1 D ec 2 01 7 Calculus of Variations with Differential Forms (2018) (1)
Sur un problème non linéaire pour la divergence et le déterminant (2015) (1)
Relaxation theorems in the calculus of variations (1980) (1)
Multiple Jacobian equations (2014) (1)
Advanced analysis for engineers. (Analyse avancée pour ingénieurs.) (2002) (1)
On the equation A∇u+∇utA=G (2020) (1)
The Case f · g > 0 (2012) (1)
The Pullback Equation (2017) (1)
Second Order Equations (1999) (1)
The Complex Eikonal Equation (1999) (1)
Sorne examples of rank one convex fonctions in dimension two (1)
Solutions to the exercises (2004) (0)
Transportation of closed differential forms with non-homogeneous convex costs (2018) (0)
On the equation (Du)H Du = G (2021) (0)
On the minimisation of non quasiconvex integrais of the calcul us of variations 1 (2013) (0)
Appendix: Piecewise Approximations (1999) (0)
Some Preliminary Results (1999) (0)
An Identity Involving Exterior Derivatives and Gaffney Inequality (2012) (0)
Comparison with Viscosity Solutions (1999) (0)
1. Introduction and examples Newton's equation of motion, Optimal consumption, Dido's problem, minimal surfaces. (2004) (0)
Relaxation for some dynamical problems (1985) (0)
The second order pullback equation (2013) (0)
The Case k = 2 (2012) (0)
The two well problem for piecewise a ¢ ne maps (2012) (0)
Volume Information (1988) (0)
General Considerations on the Flow Method (2012) (0)
Relaxation for sorne dynamical problems (0)
The degenerate two well problem for piecewise affine maps (2012) (0)
The Singular Values Case (1999) (0)
Convexity of Certain Integrais of the Calcul us of Variations-III (2013) (0)
Calculus of variations, implicit partial differential equations and microstructure (2006) (0)
An introduction to implicit partial differential equations of the first order (2001) (0)
Exterior Forms and the Notion of Divisibility (2012) (0)
The Case Without Sign Hypothesis on f (2012) (0)
Mathematical Analysis for Engineers (2012) (0)
Direct methods: regularity (2008) (0)
The Cases k = 0 and k = 1 (2012) (0)
The various stages of Nicola Fusco (2017) (0)
On a generalized Wirtinger inequality August 19 , 2002 (2003) (0)
A new approach to the existence of almost everywhere solutions of nonlinear PDEs (1998) (0)
On the equation DutHDu=G (2022) (0)
On a fractional nonlinear porous media equation in bounded domains (2015) (0)
The various stages of Nicola Fusco (Part 2) (2017) (0)
An Abstract Fixed Point Theorem (2012) (0)
Calculus of Variations The second order pullback equation (2013) (0)
The Case of Potential Wells (1999) (0)
Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms (2019) (0)
Dual and relaxed problems (1982) (0)
First Order Equations (1999) (0)
Direct methods: existence (2008) (0)
Hölder Continuous Functions (2012) (0)
Existence Theorems for Systems (1999) (0)
A variational reduction and the existence of fully localized surface with weak surface tension (2014) (0)
General Setting and the Scalar Case (1989) (0)
The Case 3 ≤ k ≤ n−1 (2012) (0)
On the Pullback Equation ${\phi }^{*}\left(g\right)=f$ (2009) (0)
Non-Convex Integrands (1989) (0)
The Equation divu = f (2012) (0)
The Hodge–Morrey Decomposition (2012) (0)
Résolution du problème de Dirichlet pour le Jacobien prescrit par l ’ équation de Monge-Ampère (0)
Existence theorems for Hamilton-Jacobi equations in the scalar and the vectorial cases. (Théorèmes d"existence dans les cas scalaireet vectoriel pour les équations de Hamilton-Jacobi.) (1996) (0)

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