Functional Analysis, Sobolev Spaces and Partial Differential Equations

This textbook is a thoroughly revised and expanded English edition of the influential French work Analyse fonctionnelle. It uniquely combines the main results from functional analysis with those from the theory of partial differential equations (PDEs), offering a coherent and unified presentation. The book is enriched with a wealth of problems and exercises, complete with solutions, to guide readers through the material. Since its initial publication, the French version has been translated into multiple languages, and this English edition is a welcome addition to the list. The book serves as an essential resource for students and researchers, providing a comprehensive overview of both functional analysis and PDEs. It is designed to be accessible yet rigorous, making it suitable for advanced undergraduate and graduate courses. The inclusion of numerous exercises ensures that readers can actively engage with the material, reinforcing their understanding of these complex topics.