{"id":"https://openalex.org/W2018800978","doi":"https://doi.org/10.1137/100784400","title":"H\u00f6lder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton\u2013Jacobi Equations with Superquadratic Growth in the Gradient","display_name":"H\u00f6lder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton\u2013Jacobi Equations with Superquadratic Growth in the Gradient","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2018800978","doi":"https://doi.org/10.1137/100784400","mag":"2018800978"},"language":"en","primary_location":{"id":"doi:10.1137/100784400","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100784400","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1001.5191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032926943","display_name":"Pierre Cardaliaguet","orcid":"https://orcid.org/0000-0002-9322-6783"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pierre Cardaliaguet","raw_affiliation_strings":["cardaliaguet@ceremade.dauphine.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"cardaliaguet@ceremade.dauphine.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007125124","display_name":"Catherine Rainer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Catherine Rainer","raw_affiliation_strings":["Catherine.Rainer@univ-brest.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"Catherine.Rainer@univ-brest.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032926943"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8751,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89484848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"49","issue":"2","first_page":"555","last_page":"573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9980000257492065,"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":0.9980000257492065,"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":0.9940000176429749,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9805999994277954,"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/mathematics","display_name":"Mathematics","score":0.8686612844467163},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.8219947218894958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6155077219009399},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5894761085510254},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5886240601539612},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5435644388198853},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.4937313497066498},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4929478168487549},{"id":"https://openalex.org/keywords/h\u00f6lder-condition","display_name":"H\u00f6lder condition","score":0.4660279452800751},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3284534811973572},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.11243808269500732},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05234640836715698}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8686612844467163},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.8219947218894958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6155077219009399},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5894761085510254},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5886240601539612},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5435644388198853},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.4937313497066498},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4929478168487549},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.4660279452800751},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3284534811973572},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.11243808269500732},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05234640836715698},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/100784400","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100784400","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1001.5191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1001.5191","pdf_url":"https://arxiv.org/pdf/1001.5191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00451248v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00451248","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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 Control and Optimization, 2011, 49 (2), pp.555-573","raw_type":"Journal articles"},{"id":"pmh:oai:basepub.dauphine.fr:123456789/5894","is_oa":false,"landing_page_url":"http://hal.archives-ouvertes.fr/hal-00451248/fr/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article accept\u00e9 pour publication ou publi\u00e9"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1001.5191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1001.5191","pdf_url":"https://arxiv.org/pdf/1001.5191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4699999988079071,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W164858608","https://openalex.org/W1542004730","https://openalex.org/W1558573846","https://openalex.org/W1580561995","https://openalex.org/W1595500633","https://openalex.org/W1640629155","https://openalex.org/W1969040483","https://openalex.org/W1970805552","https://openalex.org/W1987339106","https://openalex.org/W2026590080","https://openalex.org/W2028452538","https://openalex.org/W2032316144","https://openalex.org/W2035637414","https://openalex.org/W2040324504","https://openalex.org/W2063878212","https://openalex.org/W2073532336","https://openalex.org/W2081795476","https://openalex.org/W2088353628","https://openalex.org/W2113823823","https://openalex.org/W2145770111","https://openalex.org/W2166190603","https://openalex.org/W2588643309","https://openalex.org/W3098574159","https://openalex.org/W3105685879"],"related_works":["https://openalex.org/W1983345526","https://openalex.org/W2076944689","https://openalex.org/W2061585064","https://openalex.org/W1594944678","https://openalex.org/W1977330547","https://openalex.org/W1487586009","https://openalex.org/W3102569876","https://openalex.org/W2971079383","https://openalex.org/W2949881593","https://openalex.org/W4300025719"],"abstract_inverted_index":{"Viscosity":[0],"solutions":[1],"of":[2,32,47],"fully":[3],"nonlinear,":[4],"local":[5],"or":[6],"nonlocal,":[7],"Hamilton\u2013Jacobi":[8,43],"equations":[9,44],"with":[10,24],"a":[11,25,52],"superquadratic":[12],"growth":[13,31],"in":[14,45],"the":[15,30,33],"gradient":[16],"variable":[17],"are":[18],"proved":[19],"to":[20],"be":[21],"H\u00f6lder":[22,55],"continuous,":[23],"modulus":[26],"depending":[27],"only":[28],"on":[29],"Hamiltonian.":[34],"The":[35],"proof":[36],"involves":[37],"some":[38],"representation":[39],"formula":[40],"for":[41],"nonlocal":[42],"terms":[46],"controlled":[48],"jump":[49],"processes":[50],"and":[51],"weak":[53],"reverse":[54],"inequality.":[56]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}