Degree Theory in Analysis and Applications
Series: Oxford Lecture Series in Mathematics and Its Applications; 2;
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Product details:
- Publisher OUP Oxford
- Date of Publication 2 November 1995
- Number of Volumes laminated boards
- ISBN 9780198511960
- Binding Hardback
- No. of pages220 pages
- Size 240x161x18 mm
- Weight 472 g
- Language English 0
Categories
Short description:
The idea of extending the notion of degree to non-smooth functions came about as a result of developments in non-linear analysis. In this book Irene Fonseca and Wilfrid Gangbo consider several aspects of degree theory as applied to continuous finctions and in particular to Sobolev functions, an area in which their own recent work has won them recognition. Existing texts on degree theory approach the subject from an algebraic or topological viewpoint but in this account the emphasis is on analysis. The first chapters should be accessible to graduate students and the book as a whole provides a useful reference on recent developments in degree theory, bringing together many results that currently exist only in journals.
MoreLong description:
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.
The book brings together many results previously to be found only in journals.
Table of Contents:
Degree theory for continuous functions
Degree theory in finite dimensional spaces
Some applications of the degree theory to Topology
Measure theory and Sobolev spaces
Properties of the degree for Sobolev functions
Local invertibility of Sobolev functions. Applications
Degree in infinite dimensional spaces
References
Index
