{"id":"https://openalex.org/W4414481961","doi":"https://doi.org/10.1137/25m1726005","title":"Density Estimates for a Nonlocal Variational Model with a Degenerate Double-Well Potential via the Sobolev Inequality","display_name":"Density Estimates for a Nonlocal Variational Model with a Degenerate Double-Well Potential via the Sobolev Inequality","publication_year":2025,"publication_date":"2025-09-24","ids":{"openalex":"https://openalex.org/W4414481961","doi":"https://doi.org/10.1137/25m1726005"},"language":"en","primary_location":{"id":"doi:10.1137/25m1726005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1726005","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://api.research-repository.uwa.edu.au/ws/files/562564723/2502.13400v2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051228281","display_name":"Serena Dipierro","orcid":"https://orcid.org/0000-0003-4386-4485"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Serena Dipierro","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley, Australia"],"raw_orcid":"https://orcid.org/0000-0003-4386-4485","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002206862","display_name":"Alberto Farina","orcid":"https://orcid.org/0009-0003-6455-9161"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4647051","display_name":"Universit\u00e9 de Picardie Jules Verne","ror":"https://ror.org/01gyxrk03","country_code":"FR","type":"education","lineage":["https://openalex.org/I4647051"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alberto Farina","raw_affiliation_strings":["LAMFA, UMR CNRS, 7352 Universit\u00e9 Picardie Jules Verne 33, rue St Leu, 80039, Amiens, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMFA, UMR CNRS, 7352 Universit\u00e9 Picardie Jules Verne 33, rue St Leu, 80039, Amiens, France","institution_ids":["https://openalex.org/I4647051","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075968402","display_name":"Giovanni Giacomin","orcid":"https://orcid.org/0009-0009-8356-6715"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Giovanni Giacomin","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley, Australia"],"raw_orcid":"https://orcid.org/0009-0009-8356-6715","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078447699","display_name":"Enrico Valdinoci","orcid":"https://orcid.org/0000-0001-6222-2272"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Enrico Valdinoci","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley, Australia"],"raw_orcid":"https://orcid.org/0000-0001-6222-2272","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley, Australia","institution_ids":["https://openalex.org/I177877127"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.6896,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95927457,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"57","issue":"5","first_page":"5628","last_page":"5682"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5784000158309937},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5651999711990356},{"id":"https://openalex.org/keywords/sobolev-inequality","display_name":"Sobolev inequality","score":0.44929999113082886},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4325000047683716},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4196000099182129},{"id":"https://openalex.org/keywords/variational-method","display_name":"Variational method","score":0.3253999948501587}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.734499990940094},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5784000158309937},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5651999711990356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5296000242233276},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.44929999113082886},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4325000047683716},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32109999656677246},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/25m1726005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1726005","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/76b0179d-28b5-4193-85b1-70c6ab8f065e","is_oa":true,"landing_page_url":"https://admin.research-repository.uwa.edu.au/en/publications/76b0179d-28b5-4193-85b1-70c6ab8f065e","pdf_url":"https://api.research-repository.uwa.edu.au/ws/files/562564723/2502.13400v2.pdf","source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dipierro, S, Farina, A, Giacomin, G & Valdinoci, E 2025, 'Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality', SIAM Journal on Mathematical Analysis, vol. 57, no. 5. https://doi.org/10.1137/25M1726005","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-05285430v1","is_oa":false,"landing_page_url":"https://u-picardie.hal.science/hal-05285430","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2025, 57 (5), pp.5628-5682. ⟨10.1137/25M1726005⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/76b0179d-28b5-4193-85b1-70c6ab8f065e","is_oa":true,"landing_page_url":"https://admin.research-repository.uwa.edu.au/en/publications/76b0179d-28b5-4193-85b1-70c6ab8f065e","pdf_url":"https://api.research-repository.uwa.edu.au/ws/files/562564723/2502.13400v2.pdf","source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dipierro, S, Farina, A, Giacomin, G & Valdinoci, E 2025, 'Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality', SIAM Journal on Mathematical Analysis, vol. 57, no. 5. https://doi.org/10.1137/25M1726005","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1287761106","display_name":null,"funder_award_id":"FL190100081","funder_id":"https://openalex.org/F4320329918","funder_display_name":"Australian Mathematical Society"},{"id":"https://openalex.org/G2199393123","display_name":null,"funder_award_id":"FT230100333","funder_id":"https://openalex.org/F4320329918","funder_display_name":"Australian Mathematical Society"}],"funders":[{"id":"https://openalex.org/F4320329918","display_name":"Australian Mathematical Society","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414481961.pdf","grobid_xml":"https://content.openalex.org/works/W4414481961.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1979195399","https://openalex.org/W1990541396","https://openalex.org/W1994726900","https://openalex.org/W2001397990","https://openalex.org/W2011095781","https://openalex.org/W2024163810","https://openalex.org/W2032986113","https://openalex.org/W2033954961","https://openalex.org/W2046528357","https://openalex.org/W2048686291","https://openalex.org/W2060734843","https://openalex.org/W2074439496","https://openalex.org/W2087321746","https://openalex.org/W2132211399","https://openalex.org/W2524232970","https://openalex.org/W2949372909","https://openalex.org/W2962986974","https://openalex.org/W2963140647","https://openalex.org/W3099299356","https://openalex.org/W4254279584","https://openalex.org/W4301932427","https://openalex.org/W4321790891"],"related_works":[],"abstract_inverted_index":{"International":[0],"audience":[1]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}