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2000•Proceedings of the Edinburgh Mathematical SocietyOpen access

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

Pavel Alexandrovich Krutitskii

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Abstract

Abstract 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.

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Abstract 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.

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Available abstract

Abstract 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.

Key concepts: Laplace's equation, Mathematics, Laplace transform, Dirichlet problem, Mathematical analysis, Domain (mathematical analysis), Fredholm integral equation, Green's function for the three-variable Laplace equation

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