Degree Theory in Analysis and Applications

By: Irene Fonseca, Wilfrid Gangbo

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Hardcover | 1 December 1995

At a Glance

Hardcover
220 Pages

Dimensions(cm)
23.39 x 15.6 x 1.42

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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 for continuous 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 local invertibility 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 in the theories of ordinary differential equations and partial differential equations.

Industry Reviews

`The book brings together many results previously to be found only in journals.' Alsib Book Guide, vol.61, no.5, May 1996. `...recommended both to graduate students, as well as to more specialized researchers.' SIAM Review, Vol. 39, no.3, September 1997

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