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Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, Jyväskylä, Finland.
Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96, Göteborg, Sweden.
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, Jyväskylä, Finland.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2024 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 60, no 1, p. 387-424Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.
Place, publisher, year, edition, pages
Springer Nature , 2024. Vol. 60, no 1, p. 387-424
Keywords [en]
Acoustic equation, Helmholtz equation, Mean value theorem, Metaharmonic functions, Non-scattering phenomena, Partial balayage, Quadrature domain
National Category
Computational Mathematics Algebra and Logic Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-335758DOI: 10.1007/s11118-022-10054-5ISI: 000905599200001Scopus ID: 2-s2.0-85145025295OAI: oai:DiVA.org:kth-335758DiVA, id: diva2:1795806
Note

QC 20250520

Available from: 2023-09-11 Created: 2023-09-11 Last updated: 2025-05-20Bibliographically approved

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Shahgholian, Henrik

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