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The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts

Published online by Cambridge University Press:  20 January 2009

P. A. Krutitskii
P. A. Krutitskii
Affiliation:
Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia
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Abstract

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The Dirichlet problem for the Laplace equation in a connected-plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.

Keywords

Laplace equationDirichlet problemcracked adomain

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 325 - 341
Copyright
Copyright © Edinburgh Mathematical Society 2000

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