{"id":"https://openalex.org/W7213304521","doi":"https://doi.org/10.48550/arxiv.2609.15281","title":"A Fully Discrete Variational Approximation of Mather Measures and Sets","display_name":"A Fully Discrete Variational Approximation of Mather Measures and Sets","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213304521","doi":"https://doi.org/10.48550/arxiv.2609.15281"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15281","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15281","pdf_url":"https://arxiv.org/pdf/2609.15281","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.15281","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018541911","display_name":"Fabio Camilli","orcid":"https://orcid.org/0000-0003-2976-8112","observed_orcids":["https://orcid.org/0000-0003-2976-8112"]},"institutions":[{"id":"https://openalex.org/I39387349","display_name":"University of Chieti-Pescara","ror":"https://ror.org/00qjgza05","country_code":"IT","type":"education","lineage":["https://openalex.org/I39387349"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Camilli, Fabio","raw_affiliation_strings":["Dip. di Ingegneria e Geologia , Univ. \"G. D'Annunzio\" Chieti-Pescara , viale Pindaro 42 , 65127 Pescara ( Italy ) ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dip. di Ingegneria e Geologia , Univ. \"G. D'Annunzio\" Chieti-Pescara , viale Pindaro 42 , 65127 Pescara ( Italy ) ,","institution_ids":["https://openalex.org/I39387349"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012328242","display_name":"Cristian Mendico","orcid":"https://orcid.org/0000-0001-7674-2578","observed_orcids":["https://orcid.org/0000-0001-7674-2578"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210112333","display_name":"Institut de Math\u00e9matiques de Bourgogne","ror":"https://ror.org/021f0sa24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210112333","https://openalex.org/I4405253280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mendico, Cristian","raw_affiliation_strings":["Institut de Math\u00e9matique de Bourgogne - UMR 5584 CNRS , Universit\u00e9 Bourgogne Europe ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matique de Bourgogne - UMR 5584 CNRS , Universit\u00e9 Bourgogne Europe ,","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210112333"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.444599986076355,"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":0.444599986076355,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.10239999741315842,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.08910000324249268,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flat-torus","display_name":"flat torus","score":0.8169999718666077},{"id":"https://openalex.org/keywords/variational-approximation","display_name":"variational approximation","score":0.7519999742507935},{"id":"https://openalex.org/keywords/critical-values","display_name":"critical values","score":0.6150000095367432},{"id":"https://openalex.org/keywords/critical-solutions","display_name":"critical solution","score":0.4560000002384186},{"id":"https://openalex.org/keywords/error-estimates","display_name":"error estimates","score":0.4650000035762787},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"constrained optimization","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7401000261306763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7146000266075134},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49810001254081726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4823000133037567},{"id":"https://openalex.org/C2777964439","wikidata":"https://www.wikidata.org/wiki/Q5884201","display_name":"Holonomic","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4634999930858612},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4560000002384186},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4417000114917755},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35510000586509705},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C116721078","wikidata":"https://www.wikidata.org/wiki/Q1048005","display_name":"Holonomic constraints","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2603999972343445}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.15281","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15281","pdf_url":"https://arxiv.org/pdf/2609.15281","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"pmh:oai:HAL:hal-05750883v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05750883v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.15281","doi":"https://doi.org/10.48550/arxiv.2609.15281","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15281","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.15281","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15281","pdf_url":"https://arxiv.org/pdf/2609.15281","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213304521.pdf","grobid_xml":"https://content.openalex.org/works/W7213304521.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7157059783","https://openalex.org/W7206160120"],"related_works":["https://openalex.org/W7157059783","https://openalex.org/W2051625459","https://openalex.org/W1976848286","https://openalex.org/W2051107015","https://openalex.org/W7096074335","https://openalex.org/W2964285184","https://openalex.org/W2014608293","https://openalex.org/W3207043359","https://openalex.org/W2104296945","https://openalex.org/W2086387573"],"abstract_inverted_index":{"We":[0,42],"introduce":[1,105],"a":[2,20,34,57,106,116],"fully--discrete":[3,35,61],"variational":[4],"approximation":[5,108],"of":[6,53,60,66,95],"Mather":[7,27,62,73,89,126],"measures":[8,70],"and":[9,56,81,88],"sets":[10],"for":[11,23,48],"Tonelli":[12],"Lagrangians":[13],"on":[14,33,110],"the":[15,25,49,67,76,86,93,124],"flat":[16],"torus,":[17],"together":[18],"with":[19,38],"numerical":[21],"procedure":[22,120],"approximating":[24],"entire":[26],"set.":[28,127],"The":[29],"scheme":[30],"is":[31],"based":[32,109],"Lax--Oleinik":[36],"operator":[37],"integer":[39],"winding":[40],"labels.":[41],"prove":[43],"an":[44],"$O(\u03c4+h/\u03c4)$":[45],"error":[46],"estimate":[47],"critical":[50,54],"value,":[51],"convergence":[52,83],"solutions,":[55],"finite-dimensional":[58,117],"characterization":[59],"measures.":[63,113],"Accumulation":[64],"points":[65],"reconstructed":[68],"minimizing":[69,98],"are":[71],"continuous":[72],"measures,":[74],"while":[75],"supports":[77],"satisfy":[78],"complementary":[79],"upper":[80],"lower":[82],"results":[84],"involving":[85],"Ma\u00f1\u00e9":[87],"sets.":[90],"To":[91],"avoid":[92],"selection":[94],"only":[96],"some":[97],"components":[99],"by":[100],"exact":[101],"discrete":[102],"minimizers,":[103],"we":[104],"mass-threshold":[107],"almost-minimizing":[111],"holonomic":[112],"This":[114],"yields":[115],"constrained":[118],"optimization":[119],"designed":[121],"to":[122],"recover":[123],"whole":[125]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}