Linear and Nonlinear Functional Analysis with Applications

This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical analysis. All the basic theorems are provided with complete and detailed proofs. The author has added more than 450 pages of new material and more than 210 problems. The solutions to all of the problems will be made available on an accompanying website. Two entirely new chapters, one on locally convex spaces and distribution theory and the other on the Fourier transform and Calderón–Zygmund singular integral operators, have also been added. In addition, the chapter on the “great theorems” of nonlinear functional analysis has been enlarged and split into two chapters, one on the calculus of variations and the other on Brouwer’s theorem, Brouwer’s degree, and Leray–Schauder’s degree.

Philippe G. Ciarlet began his academic career at the Université Pierre et Marie Curie, Paris, in 1974 and then went to City University of Hong Kong from 2002 to 2022. He has been a Senior Fellow of the Hong Kong Institute for Advanced Study of City University of Hong Kong since 2015 and a Gastprofessor at the Institute for Mathematics of the University of Zürich since 2020. He is a member of nine academies, national and international, and is a SIAM Fellow and an AMS Fellow. He is the recipient of several prizes and awards, including the Poncelet Prize and a Grand Prize from the French Academy of Sciences and a Humboldt Research Award. He is Doctor Honoris Causa or Honorary Professor at thirteen universities. He is the author of more than 200 research papers and 16 books.