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Zbl 0835.35033
Krutitskii, P.A.
Dirichlet's problem for the Helmholtz equation outside cuts in a plane. (English. Russian original)
[J] Comput. Math. Math. Phys. 34, No. 8-9, 1073-1090 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 8-9, 1237-1258 (1994). ISSN 0965-5425; ISSN 1555-6662/e

Summary: The Dirichlet problem for the Helmholtz equation outside cuts in a plane is reduced to a Fredholm integral equation of the second kind, which has a unique solution for any right-hand side. An existence theorem for the classical solution of the problem is thereby proved. The solution is also unique. The behaviour of the gradient of the solution at the ends of the cuts is investigated.

MSC 2000:: *35J05 Laplace equation, etc.
35C15 Integral representations of solutions of PDE
45B05 Fredholm integral equations

Keywords: Dirichlet problem; Helmholtz equation

Cited in: Zbl 1152.35020 Zbl 1016.35015 Zbl 0888.35027

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