Pseudo-Differential Operators on Manifolds with SingularitiesBy
- B.-W. Schulze, Karl-Weierstrass-Institut für Mathematik, Berlin, Germany
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.
Studies in Mathematics and its Applications
Published: October 1991
- The Conormal Asymptotics on R+. The Mellin Transform. Spaces with Conormal Asymptotics. The Mellin Expansion of Operators. Operators on Manifolds with Conical Singularities. Spaces with Conormal Asymptotics for the Cone. The Mellin Expansions for the Cone. The Parameter-Dependent Cone Calculus. Operators on Manifolds with Edges. Preliminary Constructions. Pseudo-Differential Operators with Operator-Valued Symbols. Pseudo-Differential Operators on Manifolds with Edges. References. Index.