Degree Theory in Analysis and Applications

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Irene Fonseca (Professor of Mathematics, Professor of Mathematics, Carnegie Mellon University, Pittsburgh, USA) Wilfrid Gangbo (Postdoctoral Fellow, Postdoctoral Fellow, Mathematical Sciences Research Institute, Berkeley, California)

Degree Theory in Analysis and Applications

Irene Fonseca (Professor of Mathematics, Professor of Mathematics, Carnegie Mellon University, Pittsburgh, USA), Wilfrid Gangbo (Postdoctoral Fellow, Postdoctoral Fellow, Mathematical Sciences Research Institute, Berkeley, California), Irene Fonseca

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English

Oxford University Press
02 November 1995

Functional analysis & transforms; Differential calculus & equations; Calculus of variations; Mechanics of solids; Flow, turbulence, rheology

Series: Oxford Lecture Series in Mathematics and Its Applications

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.

By: Irene Fonseca (Professor of Mathematics Professor of Mathematics Carnegie Mellon University Pittsburgh USA), Wilfrid Gangbo (Postdoctoral Fellow, Postdoctoral Fellow, Mathematical Sciences Research Institute, Berkeley, California), Irene Fonseca
Imprint: Oxford University Press
Country of Publication: United Kingdom
Volume: 2
Dimensions: Height: 240mm, Width: 161mm, Spine: 18mm
Weight: 472g
ISBN: 9780198511960
ISBN 10: 0198511965
Series: Oxford Lecture Series in Mathematics and Its Applications
Pages: 220
Publication Date: 02 November 1995
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1: Degree theory for continuous functions 2: Degree theory in finite dimensional spaces 3: Some applications of the degree theory to Topology 4: Measure theory and Sobolev spaces 5: Properties of the degree for Sobolev functions 6: Local invertibility of Sobolev functions. Applications 7: Degree in infinite dimensional spaces References Index

Reviews for Degree Theory in Analysis and Applications

`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