{"id":"https://openalex.org/W7213291809","doi":"https://doi.org/10.48550/arxiv.2609.13722","title":"Gradient self-improvement for mixed local and nonlocal parabolic equations","display_name":"Gradient self-improvement for mixed local and nonlocal parabolic equations","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213291809","doi":"https://doi.org/10.48550/arxiv.2609.13722"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13722","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13722","pdf_url":"https://arxiv.org/pdf/2609.13722","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/2609.13722","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151764536","display_name":"Kenta Nakamura","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nakamura, Kenta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151764536"],"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":0.9800000190734863,"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":0.9800000190734863,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.010400000028312206,"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":0.003599999938160181,"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/fractional-laplacian","display_name":"fractional Laplacian","score":0.6470000147819519},{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","score":0.6830000281333923},{"id":"https://openalex.org/keywords/calderon-zygmund-decomposition","display_name":"Calder\u00f3n-Zygmund decomposition","score":0.9269999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.659600019454956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6032999753952026},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.588699996471405},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32519999146461487},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13722","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13722","pdf_url":"https://arxiv.org/pdf/2609.13722","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.2609.13722","doi":"https://doi.org/10.48550/arxiv.2609.13722","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13722","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:2609.13722","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13722","pdf_url":"https://arxiv.org/pdf/2609.13722","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/W7213291809.pdf","grobid_xml":"https://content.openalex.org/works/W7213291809.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7203661020","https://openalex.org/W7208756588"],"related_works":["https://openalex.org/W4383473391","https://openalex.org/W3037478217","https://openalex.org/W4391069623","https://openalex.org/W2284723107","https://openalex.org/W4409359465","https://openalex.org/W4393167032","https://openalex.org/W4390637854","https://openalex.org/W2305038705","https://openalex.org/W7155532992","https://openalex.org/W2793515590"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2],"new":[3],"method":[4],"for":[5,10,19,34,46],"studying":[6],"gradient":[7],"higher":[8],"integrability":[9],"mixed":[11],"local":[12,52],"and":[13,21,61,71,79],"nonlocal":[14,72],"parabolic":[15],"equations.":[16],"More":[17],"precisely,":[18],"$p>2d/(d+2)$":[20],"$s":[22],"\\in":[23,32,44],"(0,1)$,":[24],"we":[25],"prove":[26],"that":[27],"if":[28],"the":[29,69],"inhomogeneity":[30,70],"$F":[31],"L^{p(1+\u03c3)}_{\\mathrm{loc}}$":[33],"some":[35,47],"$\u03c3>0$,":[36],"then":[37],"every":[38],"weak":[39],"solution":[40],"satisfies":[41],"$\\nabla":[42],"u":[43],"L^{p(1+\\eps)}_{\\mathrm{loc}}$":[45],"$\\eps>0$,":[48],"together":[49],"with":[50],"quantitative":[51],"estimates.":[53,82],"The":[54],"proof":[55],"relies":[56],"on":[57],"stopping":[58],"time":[59],"arguments":[60],"an":[62],"intrinsic":[63],"Calder\u00f3n-Zygmund-type":[64],"covering":[65],"decomposition":[66],"in":[67],"which":[68],"energy":[73],"contributions":[74],"are":[75],"treated":[76],"by":[77],"classical":[78],"fractional":[80],"maximal":[81]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}