| Elements of Nonlinear Analysis 2000 Edition Contributor(s): Chipot, Michel (Author) |
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ISBN: 3764364068 ISBN-13: 9783764364069 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: November 2000 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Differential Equations - General |
| Dewey: 515.7 |
| LCCN: 00056481 |
| Series: Birkhäuser Advanced Texts Basler Lehrbücher |
| Physical Information: 0.78" H x 6.8" W x 9.46" (1.41 lbs) 256 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The goal of this book is to present some modern aspects of nonlinear analysis. Some of the material introduced is classical, some more exotic. We have tried to emphasize simple cases and ideas more than complicated refinements. Also, as far as possible, we present proofs that are not classical or not available in the usual literature. Of course, only a small part of nonlinear analysis is covered. Our hope is that the reader - with the help of these notes - can rapidly access the many different aspects of the field. We start by introducing two physical issues: elasticity and diffusion. The pre- sentation here is original and self contained, and helps to motivate all the rest of the book. Then we turn to some theoretical material in analysis that will be needed throughout (Chapter 2). The next six chapters are devoted to various aspects of elliptic problems. Starting with the basics of the linear theory, we introduce a first type of nonlinear problem that has today invaded the whole mathematical world: variational inequalities. In particular, in Chapter 6, we introduce a simple theory of regularity for nonlocal variational inequalities. We also attack the question of the existence, uniqueness and approximation of solutions of quasilinear and mono- tone problems (see Chapters 5, 7, 8). The material needed to read these parts is contained in Chapter 2. The arguments are explained using the simplest possible examples. |