# The Dirichlet Problem for the EquationΔu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces

Authors: P. A. Krutitskii
Journal: International Journal of Mathematics and Mathematical Sciences
 (2013)

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## Abstract

We study the Dirichlet problem for the equationΔu−k2u=0 in the exterior of nonclosed Lipschitz surfaces in R3. 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.


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## Body


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