{"id":"https://openalex.org/W2244786430","doi":"https://doi.org/10.1137/15m1029497","title":"A Transmission Problem Across a Fractal Self-Similar Interface","display_name":"A Transmission Problem Across a Fractal Self-Similar Interface","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2244786430","doi":"https://doi.org/10.1137/15m1029497","mag":"2244786430"},"language":"en","primary_location":{"id":"doi:10.1137/15m1029497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1029497","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.06674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010896193","display_name":"Yves Achdou","orcid":"https://orcid.org/0000-0002-0514-3727"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yves Achdou","raw_affiliation_strings":["LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024032465","display_name":"Thibaut Deheuvels","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":"Thibaut Deheuvels","raw_affiliation_strings":["IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)","institution_ids":["https://openalex.org/I4210161663"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9649,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89537467,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"708","last_page":"736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9940999746322632,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9940999746322632,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.8890752792358398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.670143187046051},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6624363660812378},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.616969645023346},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.6060773134231567},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5788843631744385},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.5644912123680115},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5205525159835815},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.48114264011383057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4513579308986664},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.42384272813796997},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.41051948070526123},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19337621331214905},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.055752962827682495}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.8890752792358398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.670143187046051},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6624363660812378},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.616969645023346},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.6060773134231567},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5788843631744385},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5644912123680115},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5205525159835815},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.48114264011383057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4513579308986664},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.42384272813796997},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.41051948070526123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19337621331214905},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.055752962827682495},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1029497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1029497","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1506.06674","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.06674","pdf_url":"https://arxiv.org/pdf/1506.06674","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01166411v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01166411","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":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2016, 14 (2), pp.708-736. ⟨10.1137/15M1029497⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1506.06674","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.06674","pdf_url":"https://arxiv.org/pdf/1506.06674","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":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G3597637701","display_name":"Centre de Math\u00e9matiques Henri Lebesgue : fondements, interactions, applications et Formation","funder_award_id":"ANR-11-LABX-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3851102594","display_name":"Shape Optimization","funder_award_id":"ANR-12-BS01-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6942982310","display_name":"Hamilton-Jacobi equations on heterogeneous structures and networks","funder_award_id":"ANR-12-BS01-0008","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":37,"referenced_works":["https://openalex.org/W147682785","https://openalex.org/W215950094","https://openalex.org/W278220913","https://openalex.org/W644685307","https://openalex.org/W1488877410","https://openalex.org/W1497973520","https://openalex.org/W1504907986","https://openalex.org/W1598104864","https://openalex.org/W1916618396","https://openalex.org/W1966825276","https://openalex.org/W1967476030","https://openalex.org/W1971973036","https://openalex.org/W1974001968","https://openalex.org/W1982037082","https://openalex.org/W1983145077","https://openalex.org/W1985418260","https://openalex.org/W2005915569","https://openalex.org/W2017574514","https://openalex.org/W2041505177","https://openalex.org/W2043364850","https://openalex.org/W2046337937","https://openalex.org/W2047057005","https://openalex.org/W2055310783","https://openalex.org/W2066472516","https://openalex.org/W2078742969","https://openalex.org/W2092799331","https://openalex.org/W2095401964","https://openalex.org/W2109699178","https://openalex.org/W2126881652","https://openalex.org/W2148932839","https://openalex.org/W2171979129","https://openalex.org/W2324226043","https://openalex.org/W2478351687","https://openalex.org/W2507707288","https://openalex.org/W2963677175","https://openalex.org/W3042562017","https://openalex.org/W4249775755"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W3144842310","https://openalex.org/W2206006039","https://openalex.org/W2118815061","https://openalex.org/W4297022878","https://openalex.org/W2215353002","https://openalex.org/W2354973579","https://openalex.org/W2080846028"],"abstract_inverted_index":{"We":[0,36,77],"consider":[1,38],"a":[2,58,70,157],"transmission":[3,43,64],"problem":[4,120],"in":[5,45,81,127,156],"which":[6,46,163],"the":[7,16,24,28,31,39,42,47,54,63,74,79,82,87,95,99,106,109,112,116,119,137,140,149],"interior":[8,17,32,48],"domain":[9,49],"has":[10,152],"infinitely":[11],"ramified":[12,141],"structures.":[13],"Transmission":[14],"between":[15,30],"and":[18,33,155],"exterior":[19,34],"domains":[20],"occurs":[21],"only":[22],"at":[23],"fractal":[25,75,122,150],"component":[26],"of":[27,41,61,73,84,86,98,108,111,118,139],"interface":[29,151],"domains.":[35],"also":[37],"sequence":[40],"problems":[44,93,114],"is":[50,66,134,146,167],"obtained":[51,147],"by":[52],"stopping":[53],"self-similar":[55],"construction":[56],"after":[57],"finite":[59],"number":[60],"steps;":[62],"condition":[65],"then":[67],"posed":[68],"on":[69,129,136],"prefractal":[71],"approximation":[72],"interface.":[76,123],"prove":[78],"convergence":[80,107,144],"sense":[83],"Mosco":[85],"energy":[88,96],"forms":[89],"associated":[90],"with":[91,121,160],"these":[92],"to":[94,115],"form":[97],"limit":[100],"problem.":[101],"In":[102],"particular,":[103],"this":[104],"implies":[105],"solutions":[110],"approximated":[113],"solution":[117],"The":[124,143],"proof":[125],"relies":[126],"particular":[128,158],"an":[130,164],"extension":[131,165],"property.":[132],"Emphasis":[133],"put":[135],"geometry":[138,159],"domain.":[142],"result":[145,166],"when":[148],"no":[153],"self-contact,":[154],"self-contacts,":[161],"for":[162],"proved.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}