Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792
CiteScore 2016: 0.80
SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125
Mathematical Citation Quotient (MCQ) 2015: 0.43
An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains
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 . 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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