{"id":"https://openalex.org/W2072406906","doi":"https://doi.org/10.1137/080716918","title":"Calder\u00f3n's Inverse Problem with an Imperfectly Known Boundary and Reconstruction Up to a Conformal Deformation","display_name":"Calder\u00f3n's Inverse Problem with an Imperfectly Known Boundary and Reconstruction Up to a Conformal Deformation","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2072406906","doi":"https://doi.org/10.1137/080716918","mag":"2072406906"},"language":"en","primary_location":{"id":"doi:10.1137/080716918","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080716918","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/A5009260583","display_name":"Ville Kolehmainen","orcid":"https://orcid.org/0000-0002-5621-795X"},"institutions":[{"id":"https://openalex.org/I175532246","display_name":"University of Eastern Finland","ror":"https://ror.org/00cyydd11","country_code":"FI","type":"education","lineage":["https://openalex.org/I175532246"]},{"id":"https://openalex.org/I4210107997","display_name":"Finland University","ror":"https://ror.org/014rks409","country_code":"FI","type":"education","lineage":["https://openalex.org/I4210107997"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Ville Kolehmainen","raw_affiliation_strings":["University of Eastern Finland (UEF)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Eastern Finland (UEF)","institution_ids":["https://openalex.org/I4210107997","https://openalex.org/I175532246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052627284","display_name":"Matti Lassas","orcid":"https://orcid.org/0000-0003-2043-3156"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matti Lassas","raw_affiliation_strings":["Department of Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067142392","display_name":"Petri Ola","orcid":"https://orcid.org/0000-0001-7491-2967"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petri Ola","raw_affiliation_strings":["Department of Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5925,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80717573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"3","first_page":"1371","last_page":"1381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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":0.9998999834060669,"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9966999888420105,"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/conformal-map","display_name":"Conformal map","score":0.8167827129364014},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.7287797927856445},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.724085807800293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.7054960131645203},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6375290155410767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.611091673374176},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.5414604544639587},{"id":"https://openalex.org/keywords/electrical-impedance-tomography","display_name":"Electrical impedance tomography","score":0.5296705961227417},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5212153196334839},{"id":"https://openalex.org/keywords/deformation","display_name":"Deformation (meteorology)","score":0.48574596643447876},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.47076940536499023},{"id":"https://openalex.org/keywords/conductivity","display_name":"Conductivity","score":0.43314462900161743},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.43202269077301025},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23692429065704346},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.14571964740753174},{"id":"https://openalex.org/keywords/tomography","display_name":"Tomography","score":0.14078077673912048}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.8167827129364014},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.7287797927856445},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.724085807800293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.7054960131645203},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6375290155410767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.611091673374176},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.5414604544639587},{"id":"https://openalex.org/C155175808","wikidata":"https://www.wikidata.org/wiki/Q1326472","display_name":"Electrical impedance tomography","level":3,"score":0.5296705961227417},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5212153196334839},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.48574596643447876},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47076940536499023},{"id":"https://openalex.org/C131540310","wikidata":"https://www.wikidata.org/wiki/Q907564","display_name":"Conductivity","level":2,"score":0.43314462900161743},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.43202269077301025},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23692429065704346},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.14571964740753174},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.14078077673912048},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080716918","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080716918","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1973264506","https://openalex.org/W2000532998","https://openalex.org/W2008456590","https://openalex.org/W2010923301","https://openalex.org/W2021662804","https://openalex.org/W2028788238","https://openalex.org/W2049176462","https://openalex.org/W2053305303","https://openalex.org/W2059195581","https://openalex.org/W2066780789","https://openalex.org/W2070533846","https://openalex.org/W2070803685","https://openalex.org/W2072178528","https://openalex.org/W2090590722","https://openalex.org/W2121238988","https://openalex.org/W2143227525","https://openalex.org/W2154530595","https://openalex.org/W2157877884","https://openalex.org/W2170140734","https://openalex.org/W2170164530","https://openalex.org/W2593241161","https://openalex.org/W3190906677","https://openalex.org/W4229581918"],"related_works":["https://openalex.org/W2136479075","https://openalex.org/W2098962200","https://openalex.org/W2725829804","https://openalex.org/W2120850092","https://openalex.org/W2181417489","https://openalex.org/W1982339974","https://openalex.org/W1968797734","https://openalex.org/W629372277","https://openalex.org/W1797839364","https://openalex.org/W2335426297"],"abstract_inverted_index":{"We":[0,50],"consider":[1],"two-dimensional":[2],"electrical":[3],"impedance":[4],"tomography":[5],"(EIT),":[6],"that":[7,54,106,123],"is,":[8],"the":[9,14,17,20,28,33,48,56,59,68,73,76,108,120,125,143,148,158,178],"inverse":[10],"conductivity":[11,57,117,132,155,161],"problem":[12],"in":[13,44,75,107],"case":[15],"when":[16],"boundary":[18,29,60,121],"of":[19,35,67,187],"domain":[21,69,111],"is":[22,113],"not":[23],"known.":[24],"In":[25,84,138],"this":[26,139],"case,":[27],"measurements":[30,122],"correspond":[31],"to":[32,39,47,63,119,146,163,173],"idealization":[34],"measuring":[36],"power":[37],"needed":[38],"maintain":[40],"different":[41],"voltage":[42],"configurations":[43],"electrodes":[45],"attached":[46],"boundary.":[49,83],"give":[51,174],"an":[52,80],"algorithm":[53,168],"reconstructs":[55],"from":[58],"measurement":[61],"up":[62,162],"a":[64,114,164],"conformal":[65,165],"deformation":[66],"and":[70,92,190],"estimate":[71],"quantitatively":[72],"distortion":[74],"reconstruction":[77],"caused":[78],"by":[79,196],"incorrectly":[81],"modeled":[82,110],"our":[85],"previous":[86],"results":[87],"[V.":[88],"Kolehmainen,":[89],"M.":[90],"Lassas,":[91],"P.":[93],"Ola,":[94],"SIAM":[95],"J.":[96],"Appl.":[97],"Math.,":[98],"66":[99],"(2005),":[100],"pp.":[101],"365\u2013383],":[102],"it":[103,171],"was":[104],"shown":[105],"inaccurately":[109],"there":[112],"unique":[115],"anisotropic":[116,131,150],"corresponding":[118],"has":[124],"minimal":[126],"possible":[127,172],"anisotropy.":[128],"This":[129],"minimally":[130,149],"can":[133],"be":[134],"found":[135],"using":[136],"minimization.":[137],"paper":[140],"we":[141],"use":[142],"Beltrami":[144],"equation":[145],"isotropize":[147],"conductivity.":[151],"The":[152,167,180],"obtained":[153],"isotropic":[154,160],"coincides":[156],"with":[157],"original":[159],"deformation.":[166,179],"also":[169],"makes":[170],"quantitative":[175],"estimates":[176,186],"on":[177,184,192],"proofs":[181],"are":[182],"based":[183],"H\u00f6lder":[185],"quasi-conformal":[188],"maps,":[189],"especially":[191],"precise":[193],"bounds":[194],"given":[195],"Mori's":[197],"theorem.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}