Tools and Problems in Partial Differential Equations

Thomas Alazard is a senior researcher at CNRS. For several years, he has taught partial differential equations, microlocal analysis and functional analysis at the Ecole Normale Supérieure and the Ecole Normale Supérieure Paris-Saclay. His research focuses on the applications of harmonic analysis and microlocal analysis to the study of nonlinear partial differential equations.Claude Zuily received his PhD from Université Paris-Sud (Orsay), where he was professor of mathematics until 2010. Currently emeritus professor at Université Paris-Saclay, he is the author of several books: Uniqueness and non uniqueness in the Cauchy problem (Birkhäuser 1983), Problèmes de distributions et d'équations aux dérivées partielles (Hermann 1995 and Cassini 2010), Analyse pour l'agrégation (with H. Queffélec) (Dunod 1995), Distributions et équations aux dérivées partielles (Dunod 2002). His primary areas of research are linear and nonlinear partial differentialequations.

• Part I Tools and Problems.- 1 Elements of functional analysis and distributions.- 2 Statements of the problems of Chapter 1.- 3 Functional spaces.- 4 Statements of the problems of Chapter 3.- 5 Microlocal analysis.- 6 Statements of the problems of Chapter 5.- 7 The classical equations.- 8 Statements of the problems of Chapter 7.- Part II Solutions of the Problems. A Classical results. Index.

“Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in partial differential equations may find this work useful as a summary of analytic theories published in this volume.” (Vicenţiu D. Rădulescu, zbMATH 1461.35001, 2021)