An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains
نویسندگان
چکیده
The paper is concerned with properties of an ill-posed problem for the Helmholtz equation when Dirichlet and Neumann conditions are given only on a part Γ of the boundary ∂Ω. We present an equivalent formulation of this problem in terms of a moment problem defined on the part of the boundary where no boundary conditions are imposed. Using a weak definition of the normal derivative, we prove the equivalence between these two problems for an arbitrary Lipschitz domain in R. Moreover, uniqueness of the solution is proved for the general case when Γ is a non-empty open subset of the Lipschitz boundary.
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