Jump to ContentJump to Main Navigation

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR increased in 2014: 0.880
Rank 74 out of 310 in category Mathematics and 113 out of 255 in Applied Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 0.516
Source Normalized Impact per Paper (SNIP) 2014: 1.430
Impact per Publication (IPP) 2014: 0.613

Mathematical Citation Quotient (MCQ) 2014: 0.51

VolumeIssuePage

Issues

An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains

W. Arendt1 / T. Regińska2

1Institute of Applied Analysis, University of Ulm, D-89069 Ulm, Germany. Email:

2Institute of Mathematics, Polish Academy of Sciences, 00-956 Warsaw, Poland. 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: 10.1515/JIIP.2009.041, October 2009

Publication History

Received:
2008-03-15
Published Online:
2009-10-12

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 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.

Key words.: Ill-posed problem; Helmholtz equation; Lipschitz domain; weak normal derivative; moment problem; uniqueness of the inverse problem

Citing Articles

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.

[1]
Haihua Qin and Jingmei Lu
Bulletin of the Malaysian Mathematical Sciences Society, 2015
[2]
Sergey Igorevich Kabanikhin, M. A. Shishlenin, D. B. Nurseitov, A. T. Nurseitova, and S. E. Kasenov
Journal of Applied Mathematics, 2014, Volume 2014, Page 1
[3]
F. Berntsson, V.A. Kozlov, L. Mpinganzima, and B.O. Turesson
Inverse Problems in Science and Engineering, 2014, Volume 22, Number 1, Page 45
[4]
U. Tautenhahn, U. Hämarik, B. Hofmann, and Y. Shao
Numerical Functional Analysis and Optimization, 2013, Volume 34, Number 12, Page 1370
[5]
T. Regińska and U. Tautenhahn
Numerical Functional Analysis and Optimization, 2009, Volume 30, Number 9-10, Page 1065

Comments (0)

Please log in or register to comment.