{"id":"https://openalex.org/W2052797733","doi":"https://doi.org/10.1137/120869201","title":"Lipschitz Stability of an Inverse Boundary Value Problem for a Schr\u00f6dinger-Type Equation","display_name":"Lipschitz Stability of an Inverse Boundary Value Problem for a Schr\u00f6dinger-Type Equation","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2052797733","doi":"https://doi.org/10.1137/120869201","mag":"2052797733"},"language":"en","primary_location":{"id":"doi:10.1137/120869201","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120869201","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018612168","display_name":"Elena Beretta","orcid":"https://orcid.org/0000-0002-4517-6945"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Elena Beretta","raw_affiliation_strings":["University of Rome \u201cLa Sapienza \u201d"],"affiliations":[{"raw_affiliation_string":"University of Rome \u201cLa Sapienza \u201d","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026803226","display_name":"Maarten V. de Hoop","orcid":"https://orcid.org/0000-0002-6333-0379"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maarten V. de Hoop","raw_affiliation_strings":["Purdue University"],"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059814255","display_name":"Lingyun Qiu","orcid":"https://orcid.org/0000-0002-2204-7235"},"institutions":[{"id":"https://openalex.org/I4210107842","display_name":"Institute of Mathematics and its Applications","ror":"https://ror.org/01rxg5p40","country_code":"GB","type":"education","lineage":["https://openalex.org/I4210107842"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lingyun Qiu","raw_affiliation_strings":["Institute for Mathematics and its Applications"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and its Applications","institution_ids":["https://openalex.org/I4210107842"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018612168"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":7.0043,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.97792924,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"2","first_page":"679","last_page":"699"},"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":0.9958000183105469,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8844465017318726},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8140189051628113},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.65165776014328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6090326309204102},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5969974994659424},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5650821924209595},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5229178667068481},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.49712756276130676},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.47658225893974304},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4724343717098236},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4527682065963745},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.43394118547439575},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42776668071746826},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41752520203590393},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.4163965880870819},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3262060284614563},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07552757859230042}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8844465017318726},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8140189051628113},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.65165776014328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6090326309204102},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5969974994659424},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5650821924209595},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5229178667068481},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.49712756276130676},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47658225893974304},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4724343717098236},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4527682065963745},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.43394118547439575},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42776668071746826},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41752520203590393},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4163965880870819},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3262060284614563},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07552757859230042},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/120869201","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120869201","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:CiteSeerX.psu:10.1.1.756.1237","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.1237","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1203.1650.pdf","raw_type":"text"},{"id":"pmh:oai:iris.uniroma1.it:11573/557492","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/557492","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/888790","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/888790","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W118267492","https://openalex.org/W1866311589","https://openalex.org/W1967083339","https://openalex.org/W1972581758","https://openalex.org/W1988978892","https://openalex.org/W2003175071","https://openalex.org/W2018207223","https://openalex.org/W2024375867","https://openalex.org/W2046465662","https://openalex.org/W2095463076","https://openalex.org/W3003932625","https://openalex.org/W3021722416","https://openalex.org/W3102176395"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W4294336468","https://openalex.org/W2128363130"],"abstract_inverted_index":{"In":[0,48],"this":[1,49],"paper":[2],"we":[3],"study":[4],"the":[5,12,15,19,22,34,40,60],"inverse":[6],"boundary":[7],"value":[8],"problem":[9,32],"of":[10,21,45,70],"determining":[11],"potential":[13,61],"in":[14,33],"Schr\u00f6dinger":[16],"equation":[17],"from":[18],"knowledge":[20],"Dirichlet-to-Neumann":[23],"map,":[24],"which":[25],"is":[26,44,54,62],"commonly":[27],"accepted":[28],"as":[29],"an":[30],"ill-posed":[31],"sense":[35],"that,":[36],"under":[37],"general":[38],"settings,":[39],"optimal":[41],"stability":[42,53],"estimate":[43],"logarithmic":[46],"type.":[47],"work,":[50],"a":[51,57,66],"Lipschitz-type":[52],"established":[55],"assuming":[56],"priori":[58],"that":[59],"piecewise":[63],"constant":[64],"with":[65],"bounded":[67],"known":[68],"number":[69],"unknown":[71],"values.":[72]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
