{"id":"https://openalex.org/W4415329697","doi":"https://doi.org/10.48550/arxiv.2505.16757","title":"Regularity of two-phase free boundary minimizers in periodic media","display_name":"Regularity of two-phase free boundary minimizers in periodic media","publication_year":2025,"publication_date":"2025-05-22","ids":{"openalex":"https://openalex.org/W4415329697","doi":"https://doi.org/10.48550/arxiv.2505.16757"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.16757","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.16757","pdf_url":"https://arxiv.org/pdf/2505.16757","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.16757","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022963970","display_name":"Farhan Abedin","orcid":"https://orcid.org/0000-0001-5267-4750","observed_orcids":["https://orcid.org/0000-0001-5267-4750"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abedin, Farhan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068394946","display_name":"William M. Feldman","orcid":"https://orcid.org/0000-0001-6038-4569","observed_orcids":["https://orcid.org/0000-0001-6038-4569"]},"institutions":[{"id":"https://openalex.org/I184759092","display_name":"Lafayette College","ror":"https://ror.org/036n0x007","country_code":"US","type":"education","lineage":["https://openalex.org/I184759092"]},{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feldman, William M","raw_affiliation_strings":["Department of Mathematics , Lafayette College , Easton , PA 18042","Department of Mathematics , University of Utah , Salt Lake City , UT 84112"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Lafayette College , Easton , PA 18042","institution_ids":["https://openalex.org/I184759092"]},{"raw_affiliation_string":"Department of Mathematics , University of Utah , Salt Lake City , UT 84112","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.5127000212669373,"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":0.5127000212669373,"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":0.42820000648498535,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.009600000455975533,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/two-phase-free-boundary-problem","display_name":"two-phase free boundary problem","score":0.8650000095367432},{"id":"https://openalex.org/keywords/periodic-media","display_name":"periodic media","score":0.9649999737739563},{"id":"https://openalex.org/keywords/liouville-property","display_name":"Liouville property","score":0.9419999718666077},{"id":"https://openalex.org/keywords/regularity-theory","display_name":"regularity theory","score":0.699999988079071}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7890999913215637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6710000038146973},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5849999785423279},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5813999772071838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5508000254631042},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3224000036716461},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.2644999921321869},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2505.16757","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.16757","pdf_url":"https://arxiv.org/pdf/2505.16757","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":"doi:10.48550/arxiv.2505.16757","doi":"https://doi.org/10.48550/arxiv.2505.16757","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.16757","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:2505.16757","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.16757","pdf_url":"https://arxiv.org/pdf/2505.16757","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415329697.pdf","grobid_xml":"https://content.openalex.org/works/W4415329697.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4367701341","https://openalex.org/W2910398099","https://openalex.org/W2984441394","https://openalex.org/W4400936870","https://openalex.org/W1626310618","https://openalex.org/W2953090398","https://openalex.org/W1969962191","https://openalex.org/W1947385301","https://openalex.org/W2915175668","https://openalex.org/W2617693257"],"abstract_inverted_index":{"We":[0,23],"study":[1],"the":[2,36,39],"regularity":[3],"of":[4,6,38],"minimizers":[5],"a":[7,18,32,43,47],"two-phase":[8],"energy":[9],"functional":[10],"in":[11,35],"periodic":[12],"media.":[13],"Our":[14],"main":[15],"result":[16],"is":[17,31],"large":[19],"scale":[20],"Lipschitz":[21,40],"estimate.":[22,41],"also":[24],"establish":[25],"improvement-of-flatness":[26],"for":[27,50],"non-degenerate":[28,52],"minimizers,":[29],"which":[30],"key":[33],"ingredient":[34],"proof":[37],"As":[42],"consequence,":[44],"we":[45],"obtain":[46],"Liouville":[48],"property":[49],"entire":[51],"minimizers.":[53]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2025-10-19T00:00:00"}