{"id":"https://openalex.org/W4407293711","doi":"https://doi.org/10.1137/24m165291x","title":"H\u00f6lder Regularity of Continuous Solutions to Balance Laws and Applications in the Heisenberg Group","display_name":"H\u00f6lder Regularity of Continuous Solutions to Balance Laws and Applications in the Heisenberg Group","publication_year":2025,"publication_date":"2025-02-10","ids":{"openalex":"https://openalex.org/W4407293711","doi":"https://doi.org/10.1137/24m165291x"},"language":"en","primary_location":{"id":"doi:10.1137/24m165291x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m165291x","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://hdl.handle.net/11577/3540296","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019580293","display_name":"Laura Caravenna","orcid":"https://orcid.org/0000-0001-7528-6689"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"L. Caravenna","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, 35121 Padova, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7528-6689","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, 35121 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027258831","display_name":"Elio Marconi","orcid":"https://orcid.org/0000-0003-2989-2594"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. Marconi","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, 35121 Padova, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2989-2594","affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Padova, 35121 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044990686","display_name":"Andrea Pinamonti","orcid":"https://orcid.org/0000-0003-1000-8607"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Pinamonti","raw_affiliation_strings":["Department of Mathematics, University of Trento, Trento 38123 Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Trento, Trento 38123 Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0909,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76760778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"57","issue":"1","first_page":"979","last_page":"995"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.996399998664856,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8336082696914673},{"id":"https://openalex.org/keywords/heisenberg-group","display_name":"Heisenberg group","score":0.725863516330719},{"id":"https://openalex.org/keywords/balance","display_name":"Balance (ability)","score":0.6565201878547668},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5688689351081848},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.467615008354187},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.34760934114456177},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06440222263336182}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8336082696914673},{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.725863516330719},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.6565201878547668},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5688689351081848},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.467615008354187},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.34760934114456177},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06440222263336182},{"id":"https://openalex.org/C99508421","wikidata":"https://www.wikidata.org/wiki/Q2678675","display_name":"Physical medicine and rehabilitation","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/24m165291x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m165291x","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:www.research.unipd.it:11577/3540296","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3540296","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.research.unipd.it:11577/3540296","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3540296","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5121370618","display_name":"A Lagrangian approach: from conservation laws to line-energy Ginzburg-Landau models","funder_award_id":"101025032","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"}],"funders":[{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W388957831","https://openalex.org/W1741657353","https://openalex.org/W1965371891","https://openalex.org/W1989612263","https://openalex.org/W2006103270","https://openalex.org/W2006422837","https://openalex.org/W2013030323","https://openalex.org/W2017042872","https://openalex.org/W2018464105","https://openalex.org/W2040833716","https://openalex.org/W2044139543","https://openalex.org/W2059446888","https://openalex.org/W2077431297","https://openalex.org/W2087376454","https://openalex.org/W2094192510","https://openalex.org/W2098490264","https://openalex.org/W2102561219","https://openalex.org/W2105741746","https://openalex.org/W2496430156","https://openalex.org/W2573251658","https://openalex.org/W2747704234","https://openalex.org/W2962878220","https://openalex.org/W2963582789","https://openalex.org/W2963766025","https://openalex.org/W2964267153","https://openalex.org/W3004762255","https://openalex.org/W3018002705","https://openalex.org/W3099584879","https://openalex.org/W3160900022","https://openalex.org/W3175920863","https://openalex.org/W3200743154","https://openalex.org/W4210663191","https://openalex.org/W4238313514","https://openalex.org/W4243839716","https://openalex.org/W4285803191","https://openalex.org/W4296613338","https://openalex.org/W4406772748"],"related_works":["https://openalex.org/W187158282","https://openalex.org/W2963135356","https://openalex.org/W4297817068","https://openalex.org/W1983151614","https://openalex.org/W4298848304","https://openalex.org/W299247278","https://openalex.org/W4387663351","https://openalex.org/W1607173105","https://openalex.org/W3040821467","https://openalex.org/W3004287222"],"abstract_inverted_index":{"We":[0,72],"prove":[1,41],"Ho\u0308lder":[2],"regularity":[3,56],"of":[4,29,81],"any":[5],"continuous":[6],"solution":[7],"u":[8],"to":[9,54,76],"a":[10,78],"1-D":[11],"scalar":[12],"balance":[13],"law":[14],"ut+[f(u)]x=g,":[15],"when":[16],"the":[17,24,74,82,90],"source":[18],"term":[19],"g":[20],"is":[21,27],"bounded":[22],"and":[23],"flux":[25],"f":[26],"nonlinear":[28],"order":[30],"l\u2208N":[31],"with":[32],"l\u22652.":[33],"For":[34],"example,":[35],"l=3":[36],"if":[37],"f(u)=u3.":[38],"Moreover,":[39],"we":[40],"that":[42,61],"at":[43,62],"almost":[44,63],"every":[45,64],"point":[46,65],"(t,x),":[47,66],"it":[48,67],"holds":[49,68],"u(t,x+h)\u2212u(t,x)=o(|h|1l)":[50],"as":[51,70],"h\u21920.":[52],"Due":[53],"Lipschitz":[55,87],"along":[57],"characteristics,":[58],"this":[59],"implies":[60],"u(t+k,x+h)\u2212u(t,x)=o((|h|+|k|)1l)":[69],"|(h,k)|\u21920.":[71],"apply":[73],"results":[75],"provide":[77],"new":[79],"proof":[80],"Rademacher":[83],"theorem":[84],"for":[85],"intrinsic":[86],"functions":[88],"in":[89],"first":[91],"Heisenberg":[92],"group.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
