Degree Theory in Analysis and Applications

Hardcover | April 1, 1995

byIrene Fonseca, Wilfrid Gangbo

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In this book we study the degree theory and some of its applications in analysis. It focuses on the recent developments of this theory for Sobolev functions, which distinguishes this book from the currently available literature. We begin with a thorough study of topological degree forcontinuous functions. The contents of the book include: degree theory for continuous functions, the multiplication theorem, Hopf`s theorem, Brower`s fixed point theorem, odd mappings, Jordan`s separation theorem. Following a brief review of measure theory and Sobolev functions and study localinvertibility of Sobolev functions. These results are put to use in the study variational principles in nonlinear elasticity. The Leray-Schauder degree in infinite dimensional spaces is exploited to obtain fixed point theorems. We end the book by illustrating several applications of the degree inthe theories of ordinary differential equations and partial differential equations.

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From the Publisher

In this book we study the degree theory and some of its applications in analysis. It focuses on the recent developments of this theory for Sobolev functions, which distinguishes this book from the currently available literature. We begin with a thorough study of topological degree forcontinuous functions. The contents of the book in...

Irene Fonseca is at Carnegie Mellon University, Pittsburgh. Wilfrid Gangbo is at Mathematical Sciences Research Institute, Berkeley, California.

other books by Irene Fonseca

Format:HardcoverDimensions:220 pages, 9.21 × 6.14 × 0.71 inPublished:April 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198511965

ISBN - 13:9780198511960

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Table of Contents

1. Degree theory for continuous functions2. Degree theory in finite dimensional spaces3. Some applications of the degree theory to Topology4. Measure theory and Sobolev spaces5. Properties of the degree for Sobolev functions6. Local invertibility of Sobolev functions. Applications7. Degree in infinite dimensional spacesReferencesIndex

Editorial Reviews

`...recommended both to graduate students, as well as to more specialized researchers.'SIAM Review, Vol. 39, no.3, September 1997