Abstract
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 ! of the boundary!. 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 inR d . Moreover, uniqueness of the solution is proved for the general case when ! is a non-empty open subset of the Lipschitz boundary.
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