Pseudo-Differential Operators on Manifolds with Singularities

B.-W. Schulze (Eds.)0444881379, 9780444881373, 9780080875453

The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics.
The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R + and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

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Table of contents :
Content:
Editors
Page ii

Edited by
Page iii

Copyright page
Page iv

Introduction
Pages 1-16

1. The Conormal Asymptotics on R+
Pages 17-134

2. Operators on Manifolds with Conical Singularities
Pages 135-265

3. Operators on Manifolds with Edges
Pages 266-394

References
Pages 395-401

Index
Pages 402-406

Symbol Index
Pages 407-410