Degree Theory in Analysis and Applications

Erscheinungsjahr 1995
ISBN: 978-0-19-851196-0
Verlag: OUP Oxford

Buch, Englisch, 220 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 499 g

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.

Autoren/Hrsg.

Fonseca, Gangbo

Fonseca, Irene

Gangbo, Wilfrid

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

- 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