Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition
SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712
Mathematical Citation Quotient (MCQ) 2015: 0.43
An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains
1Institute of Applied Analysis, University of Ulm, D-89069 Ulm, Germany. Email: (email)
2Institute of Mathematics, Polish Academy of Sciences, 00-956 Warsaw, Poland. Email: (email)
Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 7, Pages 703–711, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2009.041, October 2009
- Published Online:
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.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.