{"id":"https://openalex.org/W2786711461","doi":"https://doi.org/10.1137/17m1114181","title":"Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics","display_name":"Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2786711461","doi":"https://doi.org/10.1137/17m1114181","mag":"2786711461"},"language":"en","primary_location":{"id":"doi:10.1137/17m1114181","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1114181","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10486/685261","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036372371","display_name":"Jos\u00e9 C. Bellido","orcid":"https://orcid.org/0000-0001-5750-1349"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jos\u00e9 C. Bellido","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002588971","display_name":"Carlos Mora\u2010Corral","orcid":"https://orcid.org/0000-0002-2412-5508"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carlos Mora-Corral","raw_affiliation_strings":["University Aut\u00f3noma of Madrid, Faculty of Sciences, Department of Mathematics, E-28049 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-2412-5508","affiliations":[{"raw_affiliation_string":"University Aut\u00f3noma of Madrid, Faculty of Sciences, Department of Mathematics, E-28049 Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002588971"],"corresponding_institution_ids":["https://openalex.org/I63634437"],"apc_list":null,"apc_paid":null,"fwci":1.9737,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.83398267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"50","issue":"1","first_page":"779","last_page":"809"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9952999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/peridynamics","display_name":"Peridynamics","score":0.9615181684494019},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8228253722190857},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6101211905479431},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5934100151062012},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3946620225906372},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33314400911331177},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.24593332409858704},{"id":"https://openalex.org/keywords/continuum-mechanics","display_name":"Continuum mechanics","score":0.14598223567008972},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0907069742679596}],"concepts":[{"id":"https://openalex.org/C142600616","wikidata":"https://www.wikidata.org/wiki/Q4351291","display_name":"Peridynamics","level":3,"score":0.9615181684494019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8228253722190857},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6101211905479431},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5934100151062012},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3946620225906372},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33314400911331177},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.24593332409858704},{"id":"https://openalex.org/C84035572","wikidata":"https://www.wikidata.org/wiki/Q193463","display_name":"Continuum mechanics","level":2,"score":0.14598223567008972},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0907069742679596},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1114181","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1114181","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:dnet:biblosearchi::0080f4d34f7684d144501a0fd987bf70","is_oa":true,"landing_page_url":"http://hdl.handle.net/10486/685261","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dnet:biblosearchi::0080f4d34f7684d144501a0fd987bf70","is_oa":true,"landing_page_url":"http://hdl.handle.net/10486/685261","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6200000047683716,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1637319851","display_name":null,"funder_award_id":"PEII-2014-010-P","funder_id":"https://openalex.org/F4320327216","funder_display_name":"Junta de Comunidades de Castilla-La Mancha"},{"id":"https://openalex.org/G6108699521","display_name":null,"funder_award_id":"MTM2011-28198","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G6614868046","display_name":null,"funder_award_id":"RYC-2010-06125","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G6794466219","display_name":null,"funder_award_id":"PEII-2014-010-P","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6812869445","display_name":null,"funder_award_id":"RYC-2010","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G8651934409","display_name":null,"funder_award_id":"MTM2013-47053-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320327216","display_name":"Junta de Comunidades de Castilla-La Mancha","ror":"https://ror.org/02jv91m18"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W106485379","https://openalex.org/W1512048500","https://openalex.org/W1693088036","https://openalex.org/W1973127220","https://openalex.org/W1973875578","https://openalex.org/W1994183212","https://openalex.org/W1995099058","https://openalex.org/W1995655627","https://openalex.org/W2012242119","https://openalex.org/W2012828992","https://openalex.org/W2019591548","https://openalex.org/W2024238179","https://openalex.org/W2026852947","https://openalex.org/W2030579135","https://openalex.org/W2031143328","https://openalex.org/W2032188105","https://openalex.org/W2036587683","https://openalex.org/W2040048213","https://openalex.org/W2046571480","https://openalex.org/W2051916609","https://openalex.org/W2060945009","https://openalex.org/W2064845551","https://openalex.org/W2066600510","https://openalex.org/W2066970061","https://openalex.org/W2079519245","https://openalex.org/W2086063785","https://openalex.org/W2092813634","https://openalex.org/W2132565565","https://openalex.org/W2137128736","https://openalex.org/W2172034033","https://openalex.org/W2313618896","https://openalex.org/W2405506590","https://openalex.org/W2462629327","https://openalex.org/W2620978636","https://openalex.org/W3103229763"],"related_works":["https://openalex.org/W2132729321","https://openalex.org/W1993403100","https://openalex.org/W2895843456","https://openalex.org/W2956918742","https://openalex.org/W4232061221","https://openalex.org/W3013043199","https://openalex.org/W2308035364","https://openalex.org/W3013142834","https://openalex.org/W3019168637","https://openalex.org/W2412311587"],"abstract_inverted_index":{"We":[0,25,70,107],"study":[1,18],"nonlocal":[2,38,82,161],"variational":[3],"problems":[4],"in":[5,11,35,113,131,133],"$L^p$,":[6],"like":[7],"those":[8],"that":[9],"appear":[10],"peridynamics.":[12],"The":[13],"functional":[14,34],"object":[15],"of":[16,28,32,37,40,45,62,65,94,115,122,127,140],"our":[17],"is":[19,79],"given":[20],"by":[21,120],"a":[22,42,49,109,129],"double":[23],"integral.":[24],"establish":[26],"characterizations":[27],"weak":[29],"lower":[30,96,104],"semicontinuity":[31,105],"the":[33,46,59,63,77,88,92,95,103,125,138,144],"terms":[36,114],"versions":[39],"either":[41],"convexity":[43],"notion":[44],"integrand":[47],"or":[48],"Jensen":[50],"inequality":[51],"for":[52,75,99,151],"Young":[53,116],"measures.":[54],"Existence":[55],"results,":[56],"obtained":[57,80],"through":[58],"direct":[60],"method":[61],"calculus":[64],"variations,":[66],"are":[67],"also":[68],"established.":[69],"cover":[71],"different":[72],"boundary":[73],"conditions,":[74],"which":[76],"coercivity":[78],"from":[81],"Poincar\u00e9":[83],"inequalities.":[84],"Finally,":[85],"we":[86],"analyze":[87],"relaxation":[89,111,130],"(that":[90],"is,":[91],"computation":[93],"semicontinuous":[97],"envelope)":[98],"this":[100,141],"problem":[101],"when":[102],"fails.":[106],"state":[108],"general":[110],"result":[112],"measures":[117],"and":[118],"show,":[119],"means":[121],"two":[123],"examples,":[124],"difficulty":[126,142],"having":[128],"$L^p$":[132],"an":[134],"integral":[135],"form.":[136],"At":[137],"root":[139],"lies":[143],"fact":[145],"that,":[146],"contrary":[147],"to":[148,159],"what":[149],"happens":[150],"local":[152],"functionals,":[153],"nonpositive":[154],"integrands":[155],"may":[156],"give":[157],"rise":[158],"positive":[160],"functionals.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2018-02-23T00:00:00"}
