{"id":"https://openalex.org/W2610914650","doi":"https://doi.org/10.1137/18m1197308","title":"H\u00f6lder Stably Determining the Time-Dependent Electromagnetic Potential of the Schr\u00f6dinger Equation","display_name":"H\u00f6lder Stably Determining the Time-Dependent Electromagnetic Potential of the Schr\u00f6dinger Equation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2610914650","doi":"https://doi.org/10.1137/18m1197308","mag":"2610914650"},"language":"en","primary_location":{"id":"doi:10.1137/18m1197308","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1197308","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1705.01322","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032812479","display_name":"Yavar Kian","orcid":"https://orcid.org/0000-0002-5588-3600"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yavar Kian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038297320","display_name":"\u00c9ric Soccorsi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eric Soccorsi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4517,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.77261056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"2","first_page":"627","last_page":"647"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.6976271867752075},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6632498502731323},{"id":"https://openalex.org/keywords/magnetic-potential","display_name":"Magnetic potential","score":0.610682487487793},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5890077948570251},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5886854529380798},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5785039663314819},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5515515804290771},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5406811237335205},{"id":"https://openalex.org/keywords/electric-potential","display_name":"Electric potential","score":0.5110357999801636},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5074872374534607},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5037001967430115},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5011069774627686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49167996644973755},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46750080585479736},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.45939111709594727},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.457935094833374},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4261886477470398},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3666471242904663},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18423014879226685},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.15734195709228516},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1313394010066986},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.09339490532875061},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06424552202224731}],"concepts":[{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6976271867752075},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6632498502731323},{"id":"https://openalex.org/C194127275","wikidata":"https://www.wikidata.org/wiki/Q92795812","display_name":"Magnetic potential","level":3,"score":0.610682487487793},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5890077948570251},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5886854529380798},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5785039663314819},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5515515804290771},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5406811237335205},{"id":"https://openalex.org/C58570533","wikidata":"https://www.wikidata.org/wiki/Q55451","display_name":"Electric potential","level":3,"score":0.5110357999801636},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5074872374534607},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5037001967430115},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5011069774627686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49167996644973755},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46750080585479736},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.45939111709594727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.457935094833374},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4261886477470398},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3666471242904663},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18423014879226685},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.15734195709228516},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1313394010066986},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.09339490532875061},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06424552202224731},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1197308","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1197308","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1705.01322","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.01322","pdf_url":"https://arxiv.org/pdf/1705.01322","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2610914650","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1705.01322.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-01517497v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01517497","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2019, 51 (2), pp.627-647. &#x27E8;10.1137/18M1197308&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1705.01322","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1705.01322","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1705.01322","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.01322","pdf_url":"https://arxiv.org/pdf/1705.01322","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3985695424","display_name":"Multiwave Inverse Problems","funder_award_id":"ANR-17-CE40-0029","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5181360074","display_name":"ARCHIMEDE / Math\u00e9matiques","funder_award_id":"ANR-11-LABX-0033","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1488877410","https://openalex.org/W1589236075","https://openalex.org/W1723680571","https://openalex.org/W1730676475","https://openalex.org/W1949778448","https://openalex.org/W1966293189","https://openalex.org/W1972581758","https://openalex.org/W1977876940","https://openalex.org/W1978384356","https://openalex.org/W1981696101","https://openalex.org/W1990134185","https://openalex.org/W1994913287","https://openalex.org/W2003308121","https://openalex.org/W2008370032","https://openalex.org/W2009073356","https://openalex.org/W2019950961","https://openalex.org/W2020048703","https://openalex.org/W2023638857","https://openalex.org/W2031521898","https://openalex.org/W2039214741","https://openalex.org/W2047250653","https://openalex.org/W2068576165","https://openalex.org/W2073685931","https://openalex.org/W2081599046","https://openalex.org/W2083453017","https://openalex.org/W2083486756","https://openalex.org/W2093214852","https://openalex.org/W2131940854","https://openalex.org/W2139536665","https://openalex.org/W2329091197","https://openalex.org/W2398706277","https://openalex.org/W2404909774","https://openalex.org/W2469214366","https://openalex.org/W2484572294","https://openalex.org/W2592028842","https://openalex.org/W2755753363","https://openalex.org/W2963411706","https://openalex.org/W2963699209","https://openalex.org/W2963704551","https://openalex.org/W2963765525","https://openalex.org/W2963766376","https://openalex.org/W2963778024","https://openalex.org/W2964061976","https://openalex.org/W2964198642","https://openalex.org/W2964345524"],"related_works":["https://openalex.org/W2962775743","https://openalex.org/W2484572294","https://openalex.org/W3099219971","https://openalex.org/W3186979851","https://openalex.org/W2964198642","https://openalex.org/W3104415963","https://openalex.org/W1589236075","https://openalex.org/W109365803","https://openalex.org/W3122849791","https://openalex.org/W2963765525","https://openalex.org/W2094541036","https://openalex.org/W3098163807","https://openalex.org/W2123112184","https://openalex.org/W2921653207","https://openalex.org/W1496100066","https://openalex.org/W2074992093","https://openalex.org/W2109831122","https://openalex.org/W2963486026","https://openalex.org/W3025825615","https://openalex.org/W2979851579"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,7,14,29,32,43,53,60,74,77,83,87],"inverse":[3],"problem":[4,55],"of":[5,13,21,28,45,52,62,66,76],"determining":[6],"time-":[8],"and":[9,86],"space-dependent":[10],"electromagnetic":[11],"potential":[12,79,85,89],"Schr\u00f6dinger":[15],"equation":[16],"in":[17],"a":[18],"bounded":[19],"domain":[20],"$\\mathbb{R}^n$,":[22],"$n\\geq":[23],"2$,":[24],"by":[25],"boundary":[26],"observation":[27],"solution":[30],"over":[31],"entire":[33],"time":[34],"span.":[35],"In":[36],"contrast":[37],"with":[38],"published":[39],"mathematical":[40],"results":[41],"on":[42,49,71],"recovery":[44],"unknown":[46],"coefficients":[47],"depending":[48],"all":[50],"variables":[51],"Cauchy":[54],"under":[56],"consideration,":[57],"which,":[58],"to":[59],"best":[61],"our":[63],"knowledge,":[64],"are":[65],"logarithmic":[67],"type,":[68],"we":[69],"establish,":[70],"assuming":[72],"that":[73,82],"divergence":[75],"magnetic":[78,88],"is":[80],"fixed,":[81],"electric":[84],"can":[90],"be":[91],"H\u00f6lder":[92],"stably":[93],"retrieved":[94],"from":[95],"those":[96],"lateral":[97],"measurements.":[98]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2022-10-01T00:00:00"}
