{"id":"https://openalex.org/W7223053728","doi":"https://doi.org/10.48550/arxiv.2610.25740","title":"Free boundary regularity for the porous medium equation","display_name":"Free boundary regularity for the porous medium equation","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223053728","doi":"https://doi.org/10.48550/arxiv.2610.25740"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.25740","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25740","pdf_url":"https://arxiv.org/pdf/2610.25740","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/2610.25740","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159095339","display_name":"Jiakun Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Liu, Jiakun","raw_affiliation_strings":["(Jiakun Liu) School of Mathematics and Statistics , The University of Sydney , Camperdown , NSW 2006 , AUSTRALIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Jiakun Liu) School of Mathematics and Statistics , The University of Sydney , Camperdown , NSW 2006 , AUSTRALIA","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159121037","display_name":"Junqing Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Wang, Junqing","raw_affiliation_strings":["( Junqing Wang) Chern Institute of Mathematics , Nankai University , Tianjin 300071 , CHINA","(Jiakun Liu) School of Mathematics and Statistics , The University of Sydney , Camperdown , NSW 2006 , AUSTRALIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"( Junqing Wang) Chern Institute of Mathematics , Nankai University , Tianjin 300071 , CHINA","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"(Jiakun Liu) School of Mathematics and Statistics , The University of Sydney , Camperdown , NSW 2006 , AUSTRALIA","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5116116939","display_name":"Maolin Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Zhou, Maolin","raw_affiliation_strings":["(Jiakun Liu) School of Mathematics and Statistics , The University of Sydney , Camperdown , NSW 2006 , AUSTRALIA","Chern Institute of Mathematics , Nankai University , Tianjin 300071 , CHINA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Jiakun Liu) School of Mathematics and Statistics , The University of Sydney , Camperdown , NSW 2006 , AUSTRALIA","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"Chern Institute of Mathematics , Nankai University , Tianjin 300071 , CHINA","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":2,"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":0.9595000147819519,"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":0.9595000147819519,"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":0.03799999877810478,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0010000000474974513,"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/porous-medium-equation","display_name":"porous medium equation","score":0.8970000147819519},{"id":"https://openalex.org/keywords/regularity-of-free-boundary","display_name":"free boundary regularity","score":0.9750000238418579},{"id":"https://openalex.org/keywords/gradient-estimates","display_name":"gradient estimates","score":0.9409999847412109},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"maximum principle","score":0.9430000185966492},{"id":"https://openalex.org/keywords/comparison-principle","display_name":"comparison principle","score":0.7310000061988831}],"concepts":[{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.8726999759674072},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6646000146865845},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6589999794960022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6485999822616577},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.6194999814033508},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5795000195503235},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4993000030517578},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.4731999933719635},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.4593999981880188},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2743000090122223},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27300000190734863},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.2639000117778778}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.25740","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25740","pdf_url":"https://arxiv.org/pdf/2610.25740","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.2610.25740","doi":"https://doi.org/10.48550/arxiv.2610.25740","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25740","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:2610.25740","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25740","pdf_url":"https://arxiv.org/pdf/2610.25740","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/W7223053728.pdf","grobid_xml":"https://content.openalex.org/works/W7223053728.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1588713757","https://openalex.org/W1971789544","https://openalex.org/W3215119378","https://openalex.org/W2950115063","https://openalex.org/W2050034099","https://openalex.org/W2905491560","https://openalex.org/W2135684724","https://openalex.org/W2951036804","https://openalex.org/W2525925977","https://openalex.org/W2750275361"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,61],"resolve":[4],"the":[5,16,20,27,32,35,40,63,67,80],"local":[6,28],"cone":[7,29],"conjecture":[8],"proposed":[9],"by":[10],"Kienzler,":[11],"Koch,":[12],"and":[13,55],"V\u00e1zquez":[14],"concerning":[15],"free-boundary":[17],"regularity":[18],"of":[19,34,66],"porous":[21],"medium":[22],"equation.":[23],"We":[24],"prove":[25],"that":[26],"condition":[30],"guarantees":[31],"smoothness":[33,65],"free":[36,68],"boundary":[37,69],"lying":[38],"outside":[39],"initial":[41,74,81],"support.":[42],"The":[43],"proof":[44],"relies":[45],"on":[46,79],"new":[47],"gradient":[48],"estimates":[49],"obtained":[50],"through":[51],"maximum":[52],"principle":[53],"arguments":[54],"comparison":[56],"principles.":[57],"As":[58],"an":[59],"application,":[60],"establish":[62],"global-in-time":[64],"for":[70],"solutions":[71],"with":[72],"convex":[73],"support":[75],"under":[76],"standard":[77],"assumptions":[78],"data.":[82]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-21T00:00:00"}
