{"id":"https://openalex.org/W2056972463","doi":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","title":"Local Uniqueness in the Inverse Conductivity Problem with One Measurement","display_name":"Local Uniqueness in the Inverse Conductivity Problem with One Measurement","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2056972463","doi":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","mag":"2056972463"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-1995-1303113-8","doi":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","pdf_url":"https://www.ams.org/tran/1995-347-08/S0002-9947-1995-1303113-8/S0002-9947-1995-1303113-8.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/tran/1995-347-08/S0002-9947-1995-1303113-8/S0002-9947-1995-1303113-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013580565","display_name":"Giovanni Alessandrini","orcid":"https://orcid.org/0000-0002-1975-1299","observed_orcids":["https://orcid.org/0000-0002-1975-1299"]},"institutions":[{"id":"https://openalex.org/I39587148","display_name":"Wichita State University","ror":"https://ror.org/00c4e7y75","country_code":"US","type":"education","lineage":["https://openalex.org/I39587148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. Alessandrini","raw_affiliation_strings":["Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033","institution_ids":["https://openalex.org/I39587148"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064775575","display_name":"Victor Isakov","orcid":"https://orcid.org/0000-0003-2861-9393","observed_orcids":["https://orcid.org/0000-0003-2861-9393"]},"institutions":[{"id":"https://openalex.org/I39587148","display_name":"Wichita State University","ror":"https://ror.org/00c4e7y75","country_code":"US","type":"education","lineage":["https://openalex.org/I39587148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"V. Isakov","raw_affiliation_strings":["Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033","institution_ids":["https://openalex.org/I39587148"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113621455","display_name":"Jeffrey O. Powell","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I39587148","display_name":"Wichita State University","ror":"https://ror.org/00c4e7y75","country_code":"US","type":"education","lineage":["https://openalex.org/I39587148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Powell","raw_affiliation_strings":["Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033","institution_ids":["https://openalex.org/I39587148"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I39587148"],"apc_list":null,"apc_paid":null,"fwci":2.9346,"has_fulltext":true,"cited_by_count":66,"citation_normalized_percentile":{"value":0.90763828,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"347","issue":"8","first_page":"3031","last_page":"3031"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9907000064849854,"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":0.9907000064849854,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0024999999441206455,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse-conductivity-problem","display_name":"inverse conductivity problem","score":0.9879999756813049},{"id":"https://openalex.org/keywords/local-uniqueness","display_name":"local uniqueness","score":0.9700000286102295},{"id":"https://openalex.org/keywords/cauchy-data","display_name":"Cauchy data","score":0.9819999933242798},{"id":"https://openalex.org/keywords/planar-domains","display_name":"planar domains","score":0.6140000224113464},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.5210000276565552},{"id":"https://openalex.org/keywords/partial-boundary-data","display_name":"partial boundary data","score":0.515999972820282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8447952270507812},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8031876683235168},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5290364623069763},{"id":"https://openalex.org/C131540310","wikidata":"https://www.wikidata.org/wiki/Q907564","display_name":"Conductivity","level":2,"score":0.5058817267417908},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.48024895787239075},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4360949993133545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40723511576652527},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32988107204437256},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11598789691925049},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06661167740821838},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.04715251922607422},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0002-9947-1995-1303113-8","doi":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","pdf_url":"https://www.ams.org/tran/1995-347-08/S0002-9947-1995-1303113-8/S0002-9947-1995-1303113-8.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2154768","doi":"https://doi.org/10.2307/2154768","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2154768","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arts.units.it:11368/1696076","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11368/1696076","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-1995-1303113-8","doi":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1995-1303113-8","pdf_url":"https://www.ams.org/tran/1995-347-08/S0002-9947-1995-1303113-8/S0002-9947-1995-1303113-8.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1702950523","display_name":null,"funder_award_id":"W-7405","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3906074002","display_name":null,"funder_award_id":"W\u20107405\u2010Eng\u201082","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2056972463.pdf","grobid_xml":"https://content.openalex.org/works/W2056972463.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W253784358","https://openalex.org/W593349447","https://openalex.org/W604456982","https://openalex.org/W1609413062","https://openalex.org/W2003369666","https://openalex.org/W2012005558","https://openalex.org/W2024351274","https://openalex.org/W2024430140","https://openalex.org/W2044791242","https://openalex.org/W2103628339","https://openalex.org/W2151764409","https://openalex.org/W2313278888","https://openalex.org/W2470238137","https://openalex.org/W3097212141","https://openalex.org/W3112639893","https://openalex.org/W3200698245","https://openalex.org/W4239854018","https://openalex.org/W4242558706","https://openalex.org/W4300584296","https://openalex.org/W4302194290"],"related_works":["https://openalex.org/W2093892008","https://openalex.org/W2079774358","https://openalex.org/W2028152868","https://openalex.org/W295197625","https://openalex.org/W1565820747","https://openalex.org/W2334333388","https://openalex.org/W3098543326","https://openalex.org/W2103289169","https://openalex.org/W7099659495","https://openalex.org/W2070533846"],"abstract_inverted_index":{"We":[0],"prove":[1],"local":[2],"uniqueness":[3],"of":[4,35,70,73],"a":[5,21,33],"domain":[6,24],"$D$":[7],"entering":[8],"the":[9,27],"conductivity":[10],"equation":[11],"${\\text":[12],"{div}}((1":[13],"+":[14],"\\chi":[15],"(D))\\nabla":[16],"u)":[17],"=":[18],"0$":[19],"in":[20],"bounded":[22],"planar":[23],"$\\Omega$":[25],"given":[26],"Cauchy":[28],"data":[29,60],"for":[30,61],"$u$":[31,74],"on":[32,48,75],"part":[34],"$\\partial":[36,49,76],"\\Omega$.":[37,77],"The":[38],"main":[39],"assumption":[40],"is":[41,52],"that":[42],"$\\nabla":[43],"u$":[44],"has":[45],"zero":[46],"index":[47,69],"\\Omega$":[50],"which":[51],"easy":[53],"to":[54],"guarantee":[55],"by":[56],"choosing":[57],"special":[58],"boundary":[59],"$u$.":[62],"To":[63],"achieve":[64],"our":[65],"goals":[66],"we":[67],"study":[68],"critical":[71],"points":[72]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}