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Articles

The Neumann problem for the dissipative Helmholtz equation in the exterior of open Lipschitz surfaces

Pages 1677-1684 | Received 03 Mar 2012, Accepted 29 Jun 2012, Published online: 25 Sep 2012
 

Abstract

We study the Neumann problem for the dissipative Helmholtz equation in the exterior of open Lipschitz surfaces in R 3. 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 a double layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.

AMS Subject Classification:

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