Partial Differential Equations and Functional Analysis: In Memory of Pierre Grisvard (Progress in Nonlinear Differential Equations and Their Applications, 22)

Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for par­ tial differential equations with boundary conditions. He studied singulari­ ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph.D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before. Content: Front Matter....Pages i-xxii Problèmes aux limites dans des domaines avec points de rebroussement....Pages 1-17 Elliptic Problems in Domains with Edges: Anisotropic Regularity and Anisotropic Finite Element Meshes....Pages 18-34 Unique Continuation of Harmonic Functions at Boundary Points and Applications to Problems in Complex Analysis....Pages 35-40 The Wave Shaping Problem....Pages 41-59 Modélisation mathématique des coques linéairement élastiques....Pages 60-79 Fully Nonlinear Equations by Linearization and Maximal Regularity, and Applications....Pages 80-92 Strongly Elliptic Problems Near Cuspidal Points and Edges....Pages 93-110 Star produit associé � un crochet de Poisson de rang constant....Pages 111-119 La méthode des lâchés de tourbillons pour le calcul des efforts aérodynamiques....Pages 120-131 Sum of Operators’ Method in Abstract Equations....Pages 132-146 Constructive Methods for Abstract Differential Equations and Applications....Pages 147-159 On Asymptotics of Solutions of Nonlinear Second Order Elliptic Equations in Cylindrical Domains....Pages 160-173 Singularities in Solutions to Mathematical Physics Problems in Non-Smooth Domains....Pages 174-206 Problèmes sensitifs et coques élastiques minces....Pages 207-220 Contrôlabilite exacte frontière de l’équation des ondes en presence de singularités....Pages 221-234 Interpolation and Extrapolation Spaces in Evolution Equations....Pages 235-254 Localisation des singularités sur la frontière et partitions de l’unité....Pages 255-263 Back Matter....Pages 265-266 Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for parƯ tial differential equations with boundary conditions. He studied singulariƯ ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph. D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before Les problemes aux limites elliptiques dans des domaines polygonaux ou polyedraux ont ete abondamment etudies. Edited By Jean Cea, Denise Chenais, Giuseppe Geymonat, Jacques Louis Lions.