Functional analysis, Sobolev spaces and partial differential equations / Haim Brezis

A previous version of this book, originally published in 1983 in French [H. Brezis, “Analyse fonctionnelle. Théorie et applications” (Collection Mathématiques Appliquées pour la Maîtrise; Paris: Masson) (1983; Zbl 0511.46001)] and followed by numerous translations, became very popular worldwide, and was adopted as a textbook in many European universities. A deficiency of the French text was the lack of exercises. The present volume contains a wealth of problems. The author's aim is to give a systematic treatment of some of the fundamental abstract results in functional analysis and of their applications to certain concrete problems in linear differential and partial differential equations. Moreover, by interlacing extensive commentary and foreshadowing subsequent developments within the formal scheme of statements and proofs, by the inclusion of many apt examples and by appending interesting and challenging exercises, the author has written a book which is eminently suitable as a text for a graduate course. This volume is distinguished by the broad variety of problems which have been treated and by the abstract results which are developed. (Zentralblatt)

Bibliogr. p. 585-594. Index