Partial Differential Equations and Functional Analysis: In Memory of Pierre Grisvard

ISBN-13: 9781461275367 / Angielski / Miękka / 2013 / 266 str.

Cea, J.

Opis

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.

Spis treści

Problèmes aux limites dans des domaines avec points de rebroussement.- Elliptic Problems in Domains with Edges: Anisotropic Regularity and Anisotropic Finite Element Meshes.- Unique Continuation of Harmonic Functions at Boundary Points and Applications to Problems in Complex Analysis.- The Wave Shaping Problem.- Modélisation mathématique des coques linéairement élastiques.- Fully Nonlinear Equations by Linearization and Maximal Regularity and Applications.- Strongly Elliptic Problems near Cuspidal Points and Edges.- Star produit associé à un crochet de Poisson de rang constant.- La méthode des lâchées de tourbillons pour le calcul des efforts aérodynamiques.- Sum of Operators’ Method in Abstract Equations.- Constructive Methods for Abstract Differential Equations and Applications.- On Asymptotics of Solutions of Nonlinear Second Order Elliptic Equations in Cylindrical Domains.- Singularities to Solutions in Mathematical Physics Problems in Non-Smooth Domains.- Problèmes sensitifs et coques élastiques minces.- Contrôlabilite exacte frontière de l’équation des ondes en présence de singularités.- Interpolation and Extrapolation Spaces in Evolution Equations.- Localisation des singularités sur la frontière et partitions de l’unité.