{"id":"https://openalex.org/W2591587327","doi":"https://doi.org/10.3934/nhm.2018002","title":"Stochastic homogenization of maximal monotone relations and applications","display_name":"Stochastic homogenization of maximal monotone relations and applications","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2591587327","doi":"https://doi.org/10.3934/nhm.2018002","mag":"2591587327"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2018002","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018002","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=4124ae73-3217-463b-8cb4-7c5f8c51957f","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=4124ae73-3217-463b-8cb4-7c5f8c51957f","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034214738","display_name":"Luca Lussardi","orcid":"https://orcid.org/0000-0001-9130-3573"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luca Lussardi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085902619","display_name":"Stefano Marini","orcid":"https://orcid.org/0000-0002-0888-685X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefano Marini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026743594","display_name":"Marco Veneroni","orcid":"https://orcid.org/0000-0002-8526-3154"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Veneroni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034214738"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01835792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"1","first_page":"27","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9984999895095825,"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":0.9984999895095825,"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/T11558","display_name":"Composite Material Mechanics","score":0.945900022983551,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8675240278244019},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7968387603759766},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7664893865585327},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.7445540428161621},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6782191395759583},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5371132493019104},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48537933826446533},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4149460792541504},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41266074776649475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3817062973976135},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11423325538635254}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8675240278244019},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7968387603759766},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7664893865585327},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.7445540428161621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6782191395759583},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5371132493019104},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48537933826446533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4149460792541504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41266074776649475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3817062973976135},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11423325538635254},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2018002","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018002","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=4124ae73-3217-463b-8cb4-7c5f8c51957f","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:19cb095517f14ef7a5979e463c0869ee","is_oa":false,"landing_page_url":"https://doaj.org/article/19cb095517f14ef7a5979e463c0869ee","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 13, Iss 1, Pp 27-45 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2018002","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018002","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=4124ae73-3217-463b-8cb4-7c5f8c51957f","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2591587327.pdf","grobid_xml":"https://content.openalex.org/works/W2591587327.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1973510455","https://openalex.org/W2138687495","https://openalex.org/W2889856794","https://openalex.org/W1489292980","https://openalex.org/W2606574101","https://openalex.org/W2951610245","https://openalex.org/W2795079910","https://openalex.org/W1430963189","https://openalex.org/W3098536285","https://openalex.org/W2052430123"],"abstract_inverted_index":{"We":[0,41],"study":[1],"the":[2],"homogenization":[3],"of":[4,28,46],"a":[5,12],"stationary":[6],"random":[7,49],"maximal":[8],"monotone":[9,29],"operator":[10],"on":[11,24,31,37],"probability":[13],"space":[14],"equipped":[15],"with":[16,48],"an":[17],"ergodic":[18],"dynamical":[19],"system.":[20],"The":[21],"proof":[22],"relies":[23],"Fitzpatrick's":[25],"variational":[26],"formulation":[27],"relations,":[30],"Visintin's":[32],"scale":[33],"integration/disintegration":[34],"theory":[35],"and":[36,54],"Tartar-Murat's":[38],"compensated":[39],"compactness.":[40],"provide":[42],"applications":[43],"to":[44],"systems":[45],"PDEs":[47],"coefficients":[50],"arising":[51],"in":[52,55],"electromagnetism":[53],"nonlinear":[56],"elasticity.":[57]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}