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

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  • P. A. Krutitskii

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.

Suggested Citation

  • P. A. Krutitskii, 2013. "The Dirichlet Problem for the Equation in the Exterior of Nonclosed Lipschitz Surfaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-4, February.
    • Handle: RePEc:hin:jijmms:302628
    DOI: 10.1155/2013/302628
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    References listed on IDEAS

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    1. P. A. Krutitskii, 2012. "The Dirichlet Problem for the 2D Laplace Equation in a Domain with Cracks without Compatibility Conditions at Tips of the Cracks," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-20, October.
    2. P. A. Krutitskii, 2012. "The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, July.
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