{"id":"https://openalex.org/W1484495124","doi":"https://doi.org/10.1016/j.na.2015.10.023","title":"H\u00f6lder bounds and regularity of emerging free boundaries for strongly competing Schr\u00f6dinger equations with nontrivial grouping","display_name":"H\u00f6lder bounds and regularity of emerging free boundaries for strongly competing Schr\u00f6dinger equations with nontrivial grouping","publication_year":2015,"publication_date":"2015-11-29","ids":{"openalex":"https://openalex.org/W1484495124","doi":"https://doi.org/10.1016/j.na.2015.10.023","mag":"1484495124"},"language":"en","primary_location":{"id":"doi:10.1016/j.na.2015.10.023","doi":"https://doi.org/10.1016/j.na.2015.10.023","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.na.2015.10.023","pdf_url":null,"source":{"id":"https://openalex.org/S70695507","display_name":"Nonlinear Analysis","issn_l":"0362-546X","issn":["0362-546X","1873-5215"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nonlinear Analysis","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.00800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086022998","display_name":"Nicola Soave","orcid":"https://orcid.org/0000-0002-1079-5658","observed_orcids":["https://orcid.org/0000-0002-1079-5658"]},"institutions":[{"id":"https://openalex.org/I200763008","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","ror":"https://ror.org/033eqas34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200763008"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nicola Soave","raw_affiliation_strings":["Mathematisches Institut, Justus-Liebig-Universit\u00e4t Giessen, Arndtstrasse 2, 35392 Giessen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Justus-Liebig-Universit\u00e4t Giessen, Arndtstrasse 2, 35392 Giessen, Germany","institution_ids":["https://openalex.org/I200763008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075571219","display_name":"Hugo Tavares","orcid":"https://orcid.org/0000-0003-1435-7695","observed_orcids":["https://orcid.org/0000-0003-1435-7695"]},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Hugo Tavares","raw_affiliation_strings":["Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"],"raw_orcid":"https://orcid.org/0000-0003-1435-7695","affiliations":[{"raw_affiliation_string":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal","institution_ids":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042598267","display_name":"Susanna Terracini","orcid":"https://orcid.org/0000-0002-6846-7841","observed_orcids":["https://orcid.org/0000-0002-6846-7841"]},"institutions":[{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Susanna Terracini","raw_affiliation_strings":["Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 di Torino, Via Carlo Alberto, 10, 10123 Torino, Italy"],"raw_orcid":"https://orcid.org/0000-0002-6846-7841","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 di Torino, Via Carlo Alberto, 10, 10123 Torino, Italy","institution_ids":["https://openalex.org/I55143463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052274847","display_name":"Alessandro Zilio","orcid":"https://orcid.org/0000-0003-0511-363X","observed_orcids":["https://orcid.org/0000-0003-0511-363X"]},"institutions":[{"id":"https://openalex.org/I4210100624","display_name":"Centre d'Analyse et de Math\u00e9matique Sociales","ror":"https://ror.org/00vb8fc53","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210100624","https://openalex.org/I4210150854","https://openalex.org/I90669466"]},{"id":"https://openalex.org/I90669466","display_name":"\u00c9cole des hautes \u00e9tudes en sciences sociales","ror":"https://ror.org/02d9dg697","country_code":"FR","type":"facility","lineage":["https://openalex.org/I90669466"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alessandro Zilio","raw_affiliation_strings":["Centre d\u2019Analyse et de Math\u00e9matique Sociales, \u00c9cole des Hautes \u00c9tudes en Sciences Sociales, 190-198 Avenue de France, 75244, Paris CEDEX 13, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre d\u2019Analyse et de Math\u00e9matique Sociales, \u00c9cole des Hautes \u00c9tudes en Sciences Sociales, 190-198 Avenue de France, 75244, Paris CEDEX 13, France","institution_ids":["https://openalex.org/I4210100624","https://openalex.org/I90669466"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5042598267"],"corresponding_institution_ids":["https://openalex.org/I55143463"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":3.3839,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.9172973,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"138","issue":null,"first_page":"388","last_page":"427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9990000128746033,"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":0.9990000128746033,"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":0.00019999999494757503,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/holder-regularity","display_name":"H\u00f6lder regularity","score":0.8259999752044678},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"free boundary problem","score":0.6190000176429749},{"id":"https://openalex.org/keywords/nonlocal-interactions","display_name":"nonlocal interactions","score":0.4189999997615814},{"id":"https://openalex.org/keywords/sign-changing-solutions","display_name":"sign-changing solutions","score":0.5789999961853027},{"id":"https://openalex.org/keywords/bose-einstein-condensate","display_name":"Bose-Einstein condensate","score":0.9369999766349792},{"id":"https://openalex.org/keywords/elliptic-systems","display_name":"elliptic systems","score":0.5329999923706055}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7302848100662231},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6786273717880249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.597490668296814},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5564188957214355},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5440253019332886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.524178683757782},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4419684112071991},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43951216340065},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4189174473285675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2532873749732971},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2087550163269043},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1476731300354004},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1016/j.na.2015.10.023","doi":"https://doi.org/10.1016/j.na.2015.10.023","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.na.2015.10.023","pdf_url":null,"source":{"id":"https://openalex.org/S70695507","display_name":"Nonlinear Analysis","issn_l":"0362-546X","issn":["0362-546X","1873-5215"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nonlinear Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1506.00800","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.00800","pdf_url":"https://arxiv.org/pdf/1506.00800","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":"mag:1484495124","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1506.00800.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:iris.unito.it:2318/1621620","doi":null,"is_oa":false,"landing_page_url":"http://arxiv.org/abs/1211.6087","pdf_url":null,"source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/1007042","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1007042","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1506.00800","doi":"https://doi.org/10.48550/arxiv.1506.00800","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1506.00800","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:1506.00800","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.00800","pdf_url":"https://arxiv.org/pdf/1506.00800","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/G4449315702","display_name":"Centro de An\u00e1lise Matem\u00e1tica, Geometria e Sistemas Din\u00e2micos","funder_award_id":"UID/MAT/04459/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G5903895508","display_name":null,"funder_award_id":"04459/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1484495124.pdf","grobid_xml":"https://content.openalex.org/works/W1484495124.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1520256736","https://openalex.org/W1524139735","https://openalex.org/W1543974142","https://openalex.org/W1579247988","https://openalex.org/W1603289878","https://openalex.org/W1866311589","https://openalex.org/W1965667485","https://openalex.org/W1971374570","https://openalex.org/W1971583997","https://openalex.org/W1973784078","https://openalex.org/W1976354136","https://openalex.org/W1976808912","https://openalex.org/W1988644605","https://openalex.org/W2008322054","https://openalex.org/W2010613747","https://openalex.org/W2011639056","https://openalex.org/W2024890465","https://openalex.org/W2045673781","https://openalex.org/W2051692558","https://openalex.org/W2054431537","https://openalex.org/W2059557389","https://openalex.org/W2064143305","https://openalex.org/W2066823249","https://openalex.org/W2069653764","https://openalex.org/W2069691002","https://openalex.org/W2078701325","https://openalex.org/W2081083193","https://openalex.org/W2090608379","https://openalex.org/W2093716837","https://openalex.org/W2149502645","https://openalex.org/W2193983747","https://openalex.org/W2621250133","https://openalex.org/W3098432056","https://openalex.org/W3174001749"],"related_works":["https://openalex.org/W4229937407","https://openalex.org/W2963778887","https://openalex.org/W169953431","https://openalex.org/W1001507457","https://openalex.org/W3098388688","https://openalex.org/W4403746989","https://openalex.org/W7213289006","https://openalex.org/W1524139735","https://openalex.org/W2509808209","https://openalex.org/W1494066300"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}