{"id":"https://openalex.org/W2276110206","doi":"https://doi.org/10.1137/16m1106705","title":"Existence of Weak Solutions to Stationary Mean-Field Games through Variational Inequalities","display_name":"Existence of Weak Solutions to Stationary Mean-Field Games through Variational Inequalities","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2276110206","doi":"https://doi.org/10.1137/16m1106705","mag":"2276110206"},"language":"en","primary_location":{"id":"doi:10.1137/16m1106705","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106705","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1512.05828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062323947","display_name":"Rita Ferreira","orcid":"https://orcid.org/0000-0002-7169-9141"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rita Ferreira","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7169-9141","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087528940","display_name":"Diogo A. Gomes","orcid":"https://orcid.org/0000-0002-3129-3956"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diogo Gomes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062323947"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4625,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92396913,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"50","issue":"6","first_page":"5969","last_page":"6006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/variational-inequality","display_name":"Variational inequality","score":0.8826016187667847},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7906348705291748},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7790950536727905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6882845163345337},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5347653031349182},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.5025262832641602},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4179037809371948},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.41725432872772217},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38077065348625183},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3167448043823242},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10979017615318298},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0564117431640625},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05015295743942261}],"concepts":[{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.8826016187667847},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7906348705291748},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7790950536727905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6882845163345337},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5347653031349182},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.5025262832641602},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4179037809371948},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.41725432872772217},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38077065348625183},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3167448043823242},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10979017615318298},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0564117431640625},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05015295743942261}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/16m1106705","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106705","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:arXiv.org:1512.05828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.05828","pdf_url":"https://arxiv.org/pdf/1512.05828","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":null,"raw_type":"text"},{"id":"mag:2276110206","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1512.05828.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:repository.kaust.edu.sa:10754/631098","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/631098","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1512.05828","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.05828","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1512.05828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.05828","pdf_url":"https://arxiv.org/pdf/1512.05828","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":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6700000166893005,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2276110206.pdf","grobid_xml":"https://content.openalex.org/works/W2276110206.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1485289509","https://openalex.org/W1784282101","https://openalex.org/W1824203764","https://openalex.org/W1923729176","https://openalex.org/W1970717682","https://openalex.org/W1976517033","https://openalex.org/W1983321045","https://openalex.org/W1988313155","https://openalex.org/W1993228970","https://openalex.org/W1997001104","https://openalex.org/W2003988832","https://openalex.org/W2011000015","https://openalex.org/W2011435133","https://openalex.org/W2012516112","https://openalex.org/W2014608293","https://openalex.org/W2028316825","https://openalex.org/W2038686546","https://openalex.org/W2047134823","https://openalex.org/W2048138547","https://openalex.org/W2054561098","https://openalex.org/W2057470999","https://openalex.org/W2075099603","https://openalex.org/W2077743708","https://openalex.org/W2092569083","https://openalex.org/W2136003379","https://openalex.org/W2265105391","https://openalex.org/W2278819310","https://openalex.org/W2496900530","https://openalex.org/W2557843815","https://openalex.org/W2594297941","https://openalex.org/W2605856694","https://openalex.org/W2962755712","https://openalex.org/W2962775017","https://openalex.org/W2962785793","https://openalex.org/W2962951766","https://openalex.org/W2962960536","https://openalex.org/W2963552545","https://openalex.org/W2963717727","https://openalex.org/W2964128536","https://openalex.org/W2964157502"],"related_works":["https://openalex.org/W2028316825","https://openalex.org/W2011000015","https://openalex.org/W1983321045","https://openalex.org/W2964157502","https://openalex.org/W2962755712","https://openalex.org/W2057470999","https://openalex.org/W2038686546","https://openalex.org/W2017718765","https://openalex.org/W1997001104","https://openalex.org/W1993228970","https://openalex.org/W1824203764","https://openalex.org/W586490843","https://openalex.org/W2065124438","https://openalex.org/W2032323564","https://openalex.org/W1988313155","https://openalex.org/W1985506636","https://openalex.org/W1983997656","https://openalex.org/W1970717682","https://openalex.org/W1808956822","https://openalex.org/W1576577548"],"abstract_inverted_index":{"Here,":[0],"we":[1,19,33,47,59],"consider":[2],"stationary":[3,81],"monotone":[4],"mean-field":[5],"games":[6],"(MFGs)":[7],"and":[8],"study":[9],"the":[10,26,35,40,49,55,61],"existence":[11,36,50],"of":[12,37,51,63],"weak":[13,52,65,78],"solutions":[14,38,53,66,79],"induced":[15],"by":[16],"monotonicity.":[17,27],"First,":[18],"introduce":[20],"a":[21,73],"regularized":[22,41],"problem":[23],"that":[24],"preserves":[25],"Next,":[28],"using":[29,44],"variational":[30],"inequality":[31],"techniques,":[32],"prove":[34],"to":[39,76,80],"problem.":[42],"Then,":[43],"Minty's":[45],"method,":[46],"establish":[48],"for":[54],"original":[56],"MFG.":[57],"Finally,":[58],"examine":[60],"properties":[62],"these":[64],"in":[67],"several":[68],"examples.":[69],"Our":[70],"methods":[71],"provide":[72],"general":[74],"framework":[75],"construct":[77],"MFGs":[82],"with":[83],"local,":[84],"nonlocal,":[85],"or":[86],"congestion":[87],"terms.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}