{"id":"https://openalex.org/W1977491158","doi":"https://doi.org/10.1137/100806771","title":"Explicit Variational Forms for the Inverses of Integral Logarithmic Operators Over an Interval","display_name":"Explicit Variational Forms for the Inverses of Integral Logarithmic Operators Over an Interval","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1977491158","doi":"https://doi.org/10.1137/100806771","mag":"1977491158"},"language":"en","primary_location":{"id":"doi:10.1137/100806771","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100806771","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/A5030658102","display_name":"Carlos Jerez-Hanckes","orcid":"https://orcid.org/0000-0001-8225-9558"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos Jerez-Hanckes","raw_affiliation_strings":["Escuela de Ingenieria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Escuela de Ingenieria","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105687477","display_name":"Jean-Claude N\u00e9d\u00e9lec","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Claude N\u00e9d\u00e9lec","raw_affiliation_strings":["Institut de Recherche Math\u00e9matique de Rennes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche Math\u00e9matique de Rennes","institution_ids":["https://openalex.org/I4210161663"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.68,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.69314067,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"4","first_page":"2666","last_page":"2694"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7869682312011719},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5625482797622681},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5369873046875},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.531898021697998},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.49216097593307495},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.4484878480434418},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4375690817832947},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.42637595534324646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14796382188796997}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7869682312011719},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5625482797622681},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5369873046875},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.531898021697998},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.49216097593307495},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.4484878480434418},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4375690817832947},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.42637595534324646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14796382188796997}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100806771","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100806771","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:HAL:hal-01069436v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01069436","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2012, 44 (4), pp.2666-2694. &#x27E8;10.1137/100806771&#x27E9;","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":29,"referenced_works":["https://openalex.org/W198731789","https://openalex.org/W284076903","https://openalex.org/W570727756","https://openalex.org/W1522101954","https://openalex.org/W1524276732","https://openalex.org/W1552522682","https://openalex.org/W1586623601","https://openalex.org/W1602383637","https://openalex.org/W1965698827","https://openalex.org/W1967071643","https://openalex.org/W1973506540","https://openalex.org/W1977010688","https://openalex.org/W1997253006","https://openalex.org/W2001183890","https://openalex.org/W2010137567","https://openalex.org/W2010775869","https://openalex.org/W2018764087","https://openalex.org/W2059450605","https://openalex.org/W2059998776","https://openalex.org/W2065286616","https://openalex.org/W2078622074","https://openalex.org/W2089884161","https://openalex.org/W2093450271","https://openalex.org/W2123585777","https://openalex.org/W2144098834","https://openalex.org/W2170543378","https://openalex.org/W2496081756","https://openalex.org/W2911987163","https://openalex.org/W4254035729"],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2949110394","https://openalex.org/W2896134808","https://openalex.org/W4289378085","https://openalex.org/W2071055957","https://openalex.org/W4211228991","https://openalex.org/W2353790329","https://openalex.org/W3103861421","https://openalex.org/W2754495451","https://openalex.org/W2279743781"],"abstract_inverted_index":{"We":[0,56],"introduce":[1],"explicit":[2],"and":[3,11,61,69,102,106,114,134],"exact":[4],"variational":[5],"formulations":[6],"for":[7,21,122],"the":[8,27,71,99,118,123],"weakly":[9],"singular":[10],"hypersingular":[12],"operators":[13,34,101],"over":[14,129],"an":[15,59,95,130],"open":[16],"interval":[17],"as":[18,20,90],"well":[19],"their":[22,52,87],"corresponding":[23],"inverses.":[24],"Contrary":[25],"to":[26,65],"case":[28],"of":[29,117,125],"a":[30,42,112],"closed":[31],"curve,":[32],"these":[33],"no":[35],"longer":[36],"map":[37],"fractional":[38],"Sobolev":[39],"spaces":[40],"in":[41],"dual":[43],"fashion":[44],"but":[45],"degenerate":[46],"into":[47],"different":[48],"subspaces":[49],"depending":[50],"on":[51],"extensibility":[53],"by":[54,132],"zero.":[55],"show":[57],"that":[58],"average":[60],"jump":[62],"decomposition":[63],"leads":[64],"precise":[66],"coercivity":[67],"results":[68],"characterize":[70],"mismatch":[72],"occurring":[73],"between":[74,98],"associated":[75],"functional":[76],"spaces.":[77],"Through":[78],"this":[79],"setting,":[80],"we":[81,93],"naturally":[82],"define":[83],"Calder\u00f3n-type":[84],"identities":[85],"with":[86],"potential":[88],"use":[89],"preconditioners.":[91],"Moreover,":[92],"provide":[94],"interesting":[96],"relation":[97],"logarithmic":[100],"one-dimensional":[103],"Laplace":[104],"Dirichlet":[105],"Neumann":[107],"problems.":[108],"This":[109],"work":[110],"is":[111],"detailed":[113],"extended":[115],"version":[116],"article":[119],"\u201cVariational":[120],"Forms":[121],"Inverses":[124],"Integral":[126],"Logarithmic":[127],"Operators":[128],"Interval\u201d":[131],"Jerez-Hanckes":[133],"N\u00e9d\u00e9lec":[135],"[C.R.":[136],"Acad.":[137],"Sci.":[138],"Paris":[139],"Ser.":[140],"I,":[141],"349":[142],"(2011),":[143],"pp.":[144],"547--552].":[145]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
