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The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves. (English) Zbl 0910.35040

Author’s abstract: The Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed and open curves is studied. Existence of classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. Our approach holds for both internal and external domains.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
35J25 Boundary value problems for second-order elliptic equations
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