{"id":"https://openalex.org/W7220735270","doi":"https://doi.org/10.48550/arxiv.2610.06537","title":"Interior regularity of mixed local-nonlocal parabolic semilinear equations","display_name":"Interior regularity of mixed local-nonlocal parabolic semilinear equations","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220735270","doi":"https://doi.org/10.48550/arxiv.2610.06537"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06537","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06537","pdf_url":"https://arxiv.org/pdf/2610.06537","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/2610.06537","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120591937","display_name":"Sergio Junquera","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Junquera, Sergio","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada , Universidad Complutense de Madrid , Plaza de Ciencias 3 , Ciudad Universitaria , Madrid , 28040 , Madrid , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada , Universidad Complutense de Madrid , Plaza de Ciencias 3 , Ciudad Universitaria , Madrid , 28040 , Madrid , Spain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041065153","display_name":"Leandro M. Del Pezzo","orcid":"https://orcid.org/0000-0002-5263-3446","observed_orcids":["https://orcid.org/0000-0002-5263-3446"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Del Pezzo, Leandro M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.986299991607666,"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":0.986299991607666,"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":0.005100000184029341,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.003800000064074993,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/semilinear-parabolic-equations","display_name":"semilinear parabolic equations","score":0.9269999861717224},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.9710000157356262},{"id":"https://openalex.org/keywords/interior-regularity","display_name":"interior regularity","score":0.7879999876022339},{"id":"https://openalex.org/keywords/holder-continuity","display_name":"H\u00f6lder continuity","score":0.9449999928474426},{"id":"https://openalex.org/keywords/classical-solutions","display_name":"classical solutions","score":0.6620000004768372},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.8050000071525574},{"id":"https://openalex.org/keywords/dirichlet-boundary-conditions","display_name":"Dirichlet boundary conditions","score":0.8960000276565552},{"id":"https://openalex.org/keywords/nonlocal-operators","display_name":"nonlocal operators","score":0.6430000066757202}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7809000015258789},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6970999836921692},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6736000180244446},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5167999863624573},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.46560001373291016},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4607999920845032},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4514000117778778},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4359999895095825},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.38499999046325684},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.26010000705718994},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06537","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06537","pdf_url":"https://arxiv.org/pdf/2610.06537","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.2610.06537","doi":"https://doi.org/10.48550/arxiv.2610.06537","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06537","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:2610.06537","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06537","pdf_url":"https://arxiv.org/pdf/2610.06537","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":[{"id":"https://openalex.org/G103507813","display_name":null,"funder_award_id":"MCIU/AEI/ 10.13039/501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G1105844351","display_name":null,"funder_award_id":"10.13039.501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G1272900390","display_name":null,"funder_award_id":"PID2023","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G1754140167","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320310753","funder_display_name":"Agencia Nacional de Investigaci\u00f3n e Innovaci\u00f3n"},{"id":"https://openalex.org/G1787261173","display_name":null,"funder_award_id":"PID2023-148028NB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G2019505627","display_name":null,"funder_award_id":"MCIU/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G410571670","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4212894969","display_name":null,"funder_award_id":"PID2022","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G451917667","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G491712853","display_name":null,"funder_award_id":"/ AEI10.13039/501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G5539308778","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5635532810","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G7805626310","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G7863371703","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G8497050386","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320310753","display_name":"Agencia Nacional de Investigaci\u00f3n e Innovaci\u00f3n","ror":"https://ror.org/03egaj678"},{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220735270.pdf","grobid_xml":"https://content.openalex.org/works/W7220735270.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W191931854","https://openalex.org/W644710670","https://openalex.org/W1486079966","https://openalex.org/W1531503646","https://openalex.org/W1693088036","https://openalex.org/W1855169650","https://openalex.org/W2011095781","https://openalex.org/W2016697490","https://openalex.org/W2130440873","https://openalex.org/W2793367154","https://openalex.org/W3027026734","https://openalex.org/W3034624653","https://openalex.org/W3121299729","https://openalex.org/W3133606445","https://openalex.org/W3152207607","https://openalex.org/W3185855590","https://openalex.org/W4391069623","https://openalex.org/W4403403373","https://openalex.org/W4404772986","https://openalex.org/W4407085181","https://openalex.org/W4410580771"],"related_works":["https://openalex.org/W4416834182","https://openalex.org/W4406970933","https://openalex.org/W2762182542","https://openalex.org/W4391069623","https://openalex.org/W2767817072","https://openalex.org/W3016086770","https://openalex.org/W4402469196","https://openalex.org/W4404569252","https://openalex.org/W2608369241","https://openalex.org/W7147300222"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"prove":[4],"the":[5,40,47,54],"existence,":[6],"uniqueness":[7],"and":[8,23,33,44,60,70,72],"regularity":[9,56],"of":[10,14,57],"classical":[11],"solutions":[12,59],"\\break":[13,27],"a":[15,20],"semilinear":[16],"parabolic":[17],"equation":[18],"with":[19],"mixed":[21],"local":[22,49],"nonlocal":[24],"diffusion":[25],"operator":[26],"$\\mathcal{L}":[28],"=":[29],"-(-\u0394)^s":[30],"+":[31],"\u0394$":[32],"Dirichlet":[34],"boundary":[35],"conditions.":[36],"Here,":[37],"$(-\u0394)^s$":[38],"is":[39,46],"integral":[41],"fractional":[42],"laplacian":[43],"$\u0394$":[45],"classic":[48],"laplacian.":[50],"We":[51],"then":[52],"study":[53],"interior":[55],"said":[58],"conclude":[61],"that":[62],"they":[63,73],"are":[64,74],"H\u00f6lder":[65],"continuous":[66],"in":[67,76],"both":[68],"space":[69,77],"time,":[71],"$C^{2,\u03b1}_{loc}$":[75],"for":[78],"all":[79],"positive":[80],"times.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
