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Zbl 0887.35043
Krutitskii, P.A.
The Dirichlet problem for the 2-D Helmholtz equation in a multiply connected domain with cuts. (English)
[J] Z. Angew. Math. Mech. 77, No. 12, 883-890 (1997). ISSN 0044-2267; ISSN 0946-8463/e

Summary: The Dirichlet problem for the dissipative Helmholtz 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 second kind, which is uniquely solvable.
MSC 2000:
*35J25 Second order elliptic equations, boundary value problems
31A10 Integral representations of harmonic functions (two-dimensional)
35J05 Laplace equation, etc.

Keywords: classical solution; Fredholm equation

Cited in: Zbl 1181.35052

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