Recovery of L p-potential in the plane

Bibliographic Details
Main Author: Lakshtanov, Evgeny
Publication Date: 2017
Other Authors: Vainberg, Boris
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/18431
Summary: An inverse problem for the two-dimensional Schrödinger equation with Lp-potential, p>1, is considered. Using the dbar-method, the potential is recovered from the Dirichlet-to-Neumann map on the boundary of a domain containing the support of the potential. We do not assume that the potential is small or that the Faddeev scattering problem does not have exceptional points. The paper contains a new estimate on the Faddeev Green function that immediately implies the absence of exceptional points near the origin and infinity when the potential v belongs to Lp.
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spelling Recovery of L p-potential in the planeFaddeev scattering problemInverse scattering problemAn inverse problem for the two-dimensional Schrödinger equation with Lp-potential, p>1, is considered. Using the dbar-method, the potential is recovered from the Dirichlet-to-Neumann map on the boundary of a domain containing the support of the potential. We do not assume that the potential is small or that the Faddeev scattering problem does not have exceptional points. The paper contains a new estimate on the Faddeev Green function that immediately implies the absence of exceptional points near the origin and infinity when the potential v belongs to Lp.De Gruyter2017-10-02T14:55:48Z2017-10-01T00:00:00Z2017-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/18431eng1569-394510.1515/jiip-2016-0052Lakshtanov, EvgenyVainberg, Borisinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:03:00Zoai:ria.ua.pt:10773/18431Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:55:50.230943Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Recovery of L p-potential in the plane
title Recovery of L p-potential in the plane
spellingShingle Recovery of L p-potential in the plane
Lakshtanov, Evgeny
Faddeev scattering problem
Inverse scattering problem
title_short Recovery of L p-potential in the plane
title_full Recovery of L p-potential in the plane
title_fullStr Recovery of L p-potential in the plane
title_full_unstemmed Recovery of L p-potential in the plane
title_sort Recovery of L p-potential in the plane
author Lakshtanov, Evgeny
author_facet Lakshtanov, Evgeny
Vainberg, Boris
author_role author
author2 Vainberg, Boris
author2_role author
dc.contributor.author.fl_str_mv Lakshtanov, Evgeny
Vainberg, Boris
dc.subject.por.fl_str_mv Faddeev scattering problem
Inverse scattering problem
topic Faddeev scattering problem
Inverse scattering problem
description An inverse problem for the two-dimensional Schrödinger equation with Lp-potential, p>1, is considered. Using the dbar-method, the potential is recovered from the Dirichlet-to-Neumann map on the boundary of a domain containing the support of the potential. We do not assume that the potential is small or that the Faddeev scattering problem does not have exceptional points. The paper contains a new estimate on the Faddeev Green function that immediately implies the absence of exceptional points near the origin and infinity when the potential v belongs to Lp.
publishDate 2017
dc.date.none.fl_str_mv 2017-10-02T14:55:48Z
2017-10-01T00:00:00Z
2017-10-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/18431
url http://hdl.handle.net/10773/18431
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1569-3945
10.1515/jiip-2016-0052
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833594189921648640

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