On quadrature domains and an inverse problem in potential theory. (English) Zbl 0745.31002

The author considers relations between quadrature domains and the inverse problem in potential theory which are quite close and deep. He introduces some order in the class of domains determined by comparison of their potentials, studies extremal domains with respect to this order and gives some interesting examples. About the inverse problem of potential theory we refer to the recent book of the reviewer [Inverse source problems (Providence 1990; Zbl 0721.31002). There are many challenging questions there.
Reviewer: V.Isakov (Wichita)


31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
35R30 Inverse problems for PDEs


Zbl 0721.31002
Full Text: DOI


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