Synopses & Reviews
The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.
Description
Includes bibliographical references (p. [97]-103) and index.
Table of Contents
The Schwarz Principle of Reflection.
The Logarithmic Potential, Balayage, and Quadrature Domains.
Examples of ``Quadrature Identities.
Quadrature Domains: Basic Properties, 1.
Quadrature Domains: Basic Properties, 2.
Schwarzian Reflection, Revisited.
Projectors from L? (dOmega) to H? (dOmega).
The Friedrichs Operator.
Concluding Remarks.
Bibliography.
Index.