{"id":"https://openalex.org/W7213508496","doi":"https://doi.org/10.48550/arxiv.2609.18809","title":"Integral Harnack inequality and expansion of positivity for fractional porous medium equation","display_name":"Integral Harnack inequality and expansion of positivity for fractional porous medium equation","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213508496","doi":"https://doi.org/10.48550/arxiv.2609.18809"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18809","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18809","pdf_url":"https://arxiv.org/pdf/2609.18809","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2609.18809","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114424373","display_name":"Filippo Maria Cassanello","orcid":"https://orcid.org/0009-0005-3180-1497","observed_orcids":["https://orcid.org/0009-0005-3180-1497"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cassanello, Filippo Maria","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090841626","display_name":"Filomena De Filippis","orcid":"https://orcid.org/0000-0002-2784-1411","observed_orcids":["https://orcid.org/0000-0002-2784-1411"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"De Filippis, Filomena","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5120778960","display_name":"Calvin Stanko","orcid":"https://orcid.org/0009-0000-8668-3049","observed_orcids":["https://orcid.org/0009-0000-8668-3049"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stanko, Calvin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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":0.9359999895095825,"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":0.9359999895095825,"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":0.05310000106692314,"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":0.0032999999821186066,"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/fractional-porous-medium-equation","display_name":"fractional porous medium equation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.7200000286102295},{"id":"https://openalex.org/keywords/nonlocal-diffusion","display_name":"nonlocal diffusion","score":0.41100001335144043},{"id":"https://openalex.org/keywords/positivity-of-solutions","display_name":"positivity of solutions","score":0.31200000643730164}],"concepts":[{"id":"https://openalex.org/C8464174","wikidata":"https://www.wikidata.org/wiki/Q868279","display_name":"Harnack's inequality","level":2,"score":0.7721999883651733},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7192999720573425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6255999803543091},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.49720001220703125},{"id":"https://openalex.org/C163072092","wikidata":"https://www.wikidata.org/wiki/Q1135706","display_name":"Harnack's principle","level":3,"score":0.44839999079704285},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.42809998989105225},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34630000591278076},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.27889999747276306},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2508000135421753},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18809","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18809","pdf_url":"https://arxiv.org/pdf/2609.18809","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.18809","doi":"https://doi.org/10.48550/arxiv.2609.18809","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18809","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.18809","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18809","pdf_url":"https://arxiv.org/pdf/2609.18809","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G3967431365","display_name":"Gradient regularity in nonlinear nonlocal PDEs","funder_award_id":"PAT1850524","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8590477180","display_name":null,"funder_award_id":"10.55776","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213508496.pdf","grobid_xml":"https://content.openalex.org/works/W7213508496.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4376654048","https://openalex.org/W4391988008","https://openalex.org/W7131843306","https://openalex.org/W7213415431"],"related_works":["https://openalex.org/W7131909480","https://openalex.org/W2289802782","https://openalex.org/W7131622535","https://openalex.org/W2950829639","https://openalex.org/W4292603024","https://openalex.org/W2081455845","https://openalex.org/W1978357291","https://openalex.org/W2263924759","https://openalex.org/W7052244185","https://openalex.org/W7096611693"],"abstract_inverted_index":{"We":[0],"establish":[1],"an":[2],"integral":[3],"Harnack":[4],"inequality":[5],"and":[6],"expansion":[7],"of":[8],"positivity":[9],"for":[10],"solutions":[11],"to":[12],"fractional":[13],"porous":[14],"medium-type":[15],"equations":[16],"in":[17],"the":[18],"fast":[19],"diffusion":[20],"regime,":[21],"under":[22],"optimal":[23],"tail":[24],"assumptions.":[25]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-18T00:00:00"}