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On Positivity Sets for Helmholtz Solutions
Department of Mathematical Sciences, National Chengchi University, No. 64, Sec. 2, ZhiNan Rd., Wenshan District, 16302, Taipei, Taiwan, No. 64, Sec. 2, ZhiNan Rd., Wenshan District.
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, Jyväskylä, Finland, P.O. Box 35 (MaD).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2023 (English)In: Vietnam Journal of Mathematics, ISSN 2305-221X, E-ISSN 2305-2228, Vol. 51, no 4, p. 985-994Article in journal (Refereed) Published
Abstract [en]

We address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles. In particular, we show that there are solutions that are positive on the boundary of a bounded Lipschitz domain.
Place, publisher, year, edition, pages
Springer Nature , 2023. Vol. 51, no 4, p. 985-994
Keywords [en]
Acoustic equation, Helmholtz equation, Inverse scattering problem, Lipschitz domain
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-349871DOI: 10.1007/s10013-023-00646-yScopus ID: 2-s2.0-85169165799OAI: oai:DiVA.org:kth-349871DiVA, id: diva2:1882121
Note

QC 20240704

Available from: 2024-07-04 Created: 2024-07-04 Last updated: 2024-07-04Bibliographically approved

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Shahgholian, Henrik

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