Regularity of Boundaries of Quadrature Domains in Two Dimensions
Author:
- Makoto SakaiMSMakoto Sakai
- 1 March 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 24 (2) , 341-364
Abstract
First, the author discusses regularity of the boundary of a bounded quadrature domain. It is shown that the boundary is very beautiful and it consists of regular, degenerate, double, and cusp points. Next the author discusses an unbounded quadrature domain and defines its global Schwarz function, showing that it is obtained as a translation of the inversion of a bounded quadrature domain if it is not dense in the whole plane. The author gives a complete description of unbounded quadrature domains of point differential functionals of finite order and determines all null quadrature domains in two dimensions.Keywords
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