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Elements of nonlinear analysis


Chipot, Michel (2000). Elements of nonlinear analysis. Basel: Birkhäuser Verlag.

Abstract

This textbook explores the vast field of nonlinear analysis by emphasizing the underlying ideas rather than the sophisticated refinements of the theory. Two classical examples from physics, namely elasticity and diffusion, serve to motivate the theoretical parts that are then applied to various aspects of elliptic and parabolic problems. In particular, existence, uniqueness, regularity and approximation of solutions for quasilinear and monotone problems are studied, as well as some new aspects of the calculus of variations including Young measures or approximation of minimizing sequences. The book is reasonably self-contained. Wherever possible, original proofs are given that are not to be found elsewhere. The text is geared towards graduate students and nonspecialists in nonlinear analysis who wish to become acquainted with the basic ideas of the subject. The study of this book will enable the reader to access the many ramifications of the field.

Abstract

This textbook explores the vast field of nonlinear analysis by emphasizing the underlying ideas rather than the sophisticated refinements of the theory. Two classical examples from physics, namely elasticity and diffusion, serve to motivate the theoretical parts that are then applied to various aspects of elliptic and parabolic problems. In particular, existence, uniqueness, regularity and approximation of solutions for quasilinear and monotone problems are studied, as well as some new aspects of the calculus of variations including Young measures or approximation of minimizing sequences. The book is reasonably self-contained. Wherever possible, original proofs are given that are not to be found elsewhere. The text is geared towards graduate students and nonspecialists in nonlinear analysis who wish to become acquainted with the basic ideas of the subject. The study of this book will enable the reader to access the many ramifications of the field.

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Additional indexing

Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:compactness method; partial differential equations; elliptic problems; parabolic problems; calculus of variations; monotonicity method; regularity for nonlocal variational inequalities; finite element method for elliptic problems
Language:English
Date:2000
Deposited On:17 Nov 2009 15:05
Last Modified:19 Feb 2018 22:17
Publisher:Birkhäuser Verlag
Series Name:Birkhäuser Advanced Texts: Basler Lehrbücher.
Number of Pages:256
ISBN:3-7643-6406-8
OA Status:Closed
Official URL:http://www.springer.com/birkhauser/mathematics/book/978-3-7643-6406-9
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1801735
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0964.35002

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