The Dirichlet Problem for the Equation in the Exterior of Nonclosed Lipschitz Surfaces

P. A. Krutitskii

International Journal of Mathematics and Mathematical Sciences, 2013, vol. 2013, 1-4

Abstract:

We study the Dirichlet problem for the equation in the exterior of nonclosed Lipschitz surfaces in . The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:302628

DOI: 10.1155/2013/302628

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