On Positivity Sets for Helmholtz Solutions

Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik

doi:10.1007/s10013-023-00646-y

dc.contributor.author	Kow, Pu-Zhao
dc.contributor.author	Salo, Mikko
dc.contributor.author	Shahgholian, Henrik
dc.date.accessioned	2023-09-07T07:25:20Z
dc.date.available	2023-09-07T07:25:20Z
dc.date.issued	2023
dc.identifier.citation	Kow, P.-Z., Salo, M., & Shahgholian, H. (2023). On Positivity Sets for Helmholtz Solutions. <i>Vietnam Journal of Mathematics</i>, <i>51</i>(4), 985-994. <a href="https://doi.org/10.1007/s10013-023-00646-y" target="_blank">https://doi.org/10.1007/s10013-023-00646-y</a>
dc.identifier.other	CONVID_184653719
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/88937
dc.description.abstract	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.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Springer
dc.relation.ispartofseries	Vietnam Journal of Mathematics
dc.rights	CC BY 4.0
dc.subject.other	Helmholtz equation
dc.subject.other	acoustic equation
dc.subject.other	Lipschitz domain
dc.subject.other	inverse scattering problem
dc.title	On Positivity Sets for Helmholtz Solutions
dc.type	research article
dc.identifier.urn	URN:NBN:fi:jyu-202309074970
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Inversio-ongelmien huippuyksikkö	fi
dc.contributor.oppiaine	Mathematics	en
dc.contributor.oppiaine	Centre of Excellence in Inverse Problems	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	985-994
dc.relation.issn	2305-221X
dc.relation.numberinseries	4
dc.relation.volume	51
dc.type.version	publishedVersion
dc.rights.copyright	© 2023 the Authors
dc.rights.accesslevel	openAccess	fi
dc.type.publication	article
dc.relation.grantnumber	770924
dc.relation.grantnumber	770924
dc.relation.grantnumber	312121
dc.relation.projectid	info:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified
dc.subject.yso	osittaisdifferentiaaliyhtälöt
dc.subject.yso	inversio-ongelmat
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p12392
jyx.subject.uri	http://www.yso.fi/onto/yso/p27912
dc.rights.url	https://creativecommons.org/licenses/by/4.0/
dc.relation.doi	10.1007/s10013-023-00646-y
dc.relation.funder	European Commission	en
dc.relation.funder	Research Council of Finland	en
dc.relation.funder	Euroopan komissio	fi
dc.relation.funder	Suomen Akatemia	fi
jyx.fundingprogram	ERC Consolidator Grant	en
jyx.fundingprogram	Centre of Excellence, AoF	en
jyx.fundingprogram	ERC Consolidator Grant	fi
jyx.fundingprogram	Huippuyksikkörahoitus, SA	fi
jyx.fundinginformation	This project was finalized while the authors stayed at Institute Mittag Leffler (Sweden), during the program Geometric aspects of nonlinear PDE. Kow and Salo were partly supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, 312121) and by the European Research Council under Horizon 2020 (ERC CoG 770924). Shahgholian was supported by Swedish Research Council.
dc.type.okm	A1