{"id":"https://openalex.org/W1995099058","doi":"https://doi.org/10.1137/130911548","title":"Existence for Nonlocal Variational Problems in Peridynamics","display_name":"Existence for Nonlocal Variational Problems in Peridynamics","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1995099058","doi":"https://doi.org/10.1137/130911548","mag":"1995099058"},"language":"en","primary_location":{"id":"doi:10.1137/130911548","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911548","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/A5036372371","display_name":"Jos\u00e9 C. Bellido","orcid":"https://orcid.org/0000-0001-5750-1349"},"institutions":[{"id":"https://openalex.org/I79189158","display_name":"University of Castilla-La Mancha","ror":"https://ror.org/05r78ng12","country_code":"ES","type":"education","lineage":["https://openalex.org/I79189158"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 C. Bellido","raw_affiliation_strings":["University of Castilla-La Mancha#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Castilla-La Mancha#TAB#","institution_ids":["https://openalex.org/I79189158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002588971","display_name":"Carlos Mora\u2010Corral","orcid":"https://orcid.org/0000-0002-2412-5508"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos Mora-Corral","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036372371"],"corresponding_institution_ids":["https://openalex.org/I79189158"],"apc_list":null,"apc_paid":null,"fwci":5.5955,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.95389312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"46","issue":"1","first_page":"890","last_page":"916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":1.0,"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":1.0,"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":0.9986000061035156,"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":0.9905999898910522,"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":0.9030816555023193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7983500957489014},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6713343858718872},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5931831002235413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5547508001327515},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4504736363887787},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.4270970821380615},{"id":"https://openalex.org/keywords/continuum-mechanics","display_name":"Continuum mechanics","score":0.28386497497558594},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.22444647550582886}],"concepts":[{"id":"https://openalex.org/C142600616","wikidata":"https://www.wikidata.org/wiki/Q4351291","display_name":"Peridynamics","level":3,"score":0.9030816555023193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7983500957489014},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6713343858718872},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5931831002235413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5547508001327515},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4504736363887787},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.4270970821380615},{"id":"https://openalex.org/C84035572","wikidata":"https://www.wikidata.org/wiki/Q193463","display_name":"Continuum mechanics","level":2,"score":0.28386497497558594},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.22444647550582886},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130911548","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911548","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W106485379","https://openalex.org/W585462275","https://openalex.org/W1480714962","https://openalex.org/W1486079966","https://openalex.org/W1508861003","https://openalex.org/W1512048500","https://openalex.org/W1537639429","https://openalex.org/W1569512514","https://openalex.org/W1618893934","https://openalex.org/W1639449914","https://openalex.org/W1665380423","https://openalex.org/W1865995933","https://openalex.org/W1963987355","https://openalex.org/W1973127220","https://openalex.org/W1973875578","https://openalex.org/W1993193430","https://openalex.org/W1994183212","https://openalex.org/W2007393042","https://openalex.org/W2011095781","https://openalex.org/W2012242119","https://openalex.org/W2012828992","https://openalex.org/W2019591548","https://openalex.org/W2024238179","https://openalex.org/W2026852947","https://openalex.org/W2029529153","https://openalex.org/W2036587683","https://openalex.org/W2038649727","https://openalex.org/W2046571480","https://openalex.org/W2060945009","https://openalex.org/W2064845551","https://openalex.org/W2066500222","https://openalex.org/W2066600510","https://openalex.org/W2066970061","https://openalex.org/W2079519245","https://openalex.org/W2086926544","https://openalex.org/W2087584322","https://openalex.org/W2097854981","https://openalex.org/W2143206135","https://openalex.org/W2313618896","https://openalex.org/W2477542318","https://openalex.org/W2620978636","https://openalex.org/W2950086956","https://openalex.org/W2964038482"],"related_works":["https://openalex.org/W2132729321","https://openalex.org/W1993403100","https://openalex.org/W2895843456","https://openalex.org/W2956918742","https://openalex.org/W3013043199","https://openalex.org/W2308035364","https://openalex.org/W3013142834","https://openalex.org/W4380203312","https://openalex.org/W4232061221","https://openalex.org/W4247721526"],"abstract_inverted_index":{"We":[0,31,71],"present":[1],"an":[2],"existence":[3,80],"theory":[4,81],"based":[5],"on":[6],"minimization":[7],"of":[8,28,36,39,46,49],"the":[9,26,33,37,47,85,91],"nonlocal":[10,18,68],"energies":[11],"appearing":[12],"in":[13,21,41,84,90],"peridynamics,":[14],"which":[15],"is":[16,54,64,82],"a":[17,50,57,67],"continuum":[19],"model":[20],"solid":[22],"mechanics":[23],"that":[24],"avoids":[25],"use":[27],"deformation":[29],"gradients.":[30],"employ":[32],"direct":[34],"method":[35],"calculus":[38],"variations":[40],"order":[42],"to":[43],"find":[44],"minimizers":[45],"energy":[48],"deformation.":[51],"Lower":[52],"semicontinuity":[53],"proved":[55,65],"under":[56],"weaker":[58],"condition":[59],"than":[60],"convexity,":[61],"whereas":[62],"coercivity":[63],"via":[66],"Poincar\u00e9":[69],"inequality.":[70],"cover":[72],"Dirichlet,":[73],"Neumann,":[74],"and":[75,89,102],"mixed":[76],"boundary":[77],"conditions.":[78],"The":[79],"set":[83],"Lebesgue":[86],"$L^p$":[87],"spaces":[88],"fractional":[92],"Sobolev":[93],"$W^{s,p}$":[94],"spaces,":[95],"for":[96],"$0":[97],"<":[98,100,104,106],"s":[99],"1$":[101],"$1":[103],"p":[105],"\\infty$.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
