{"id":"https://openalex.org/W2073532336","doi":"https://doi.org/10.1137/s0363012904440897","title":"Uniqueness Results for Second-Order Bellman--Isaacs Equations under Quadratic Growth Assumptions and Applications","display_name":"Uniqueness Results for Second-Order Bellman--Isaacs Equations under Quadratic Growth Assumptions and Applications","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2073532336","doi":"https://doi.org/10.1137/s0363012904440897","mag":"2073532336"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012904440897","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012904440897","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/1002.2373","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110928738","display_name":"Francesca Da Lio","orcid":null},"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":"Francesca Da Lio","raw_affiliation_strings":["Dipartimento di Matematica Pura e Applicata [Padova] (Via Trieste, 63 35121 Padova - Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura e Applicata [Padova] (Via Trieste, 63 35121 Padova - Italy)","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012309630","display_name":"Olivier Ley","orcid":"https://orcid.org/0009-0000-4579-3698"},"institutions":[{"id":"https://openalex.org/I4210132217","display_name":"Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique","ror":"https://ror.org/03g2c2k71","country_code":"FR","type":"facility","lineage":["https://openalex.org/I110017253","https://openalex.org/I1294671590","https://openalex.org/I4210132217","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Ley","raw_affiliation_strings":["IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)","LMPT - Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (Avenue Monge Parc de Grandmont - 37200 Tours - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)","institution_ids":["https://openalex.org/I4210161663"]},{"raw_affiliation_string":"LMPT - Laboratoire de Math\u00e9matiques et Physique Th\u00e9orique (Avenue Monge Parc de Grandmont - 37200 Tours - France)","institution_ids":["https://openalex.org/I4210132217"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4091,"has_fulltext":false,"cited_by_count":87,"citation_normalized_percentile":{"value":0.94360087,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"74","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9753999710083008,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.88717120885849},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.8385037183761597},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8328919410705566},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.8204822540283203},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.8128429651260376},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6306415796279907},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.5893464088439941},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5742952227592468},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5572049021720886},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.49581608176231384},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4801068603992462},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.46858829259872437},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4432207942008972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4326721727848053},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.296866238117218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.88717120885849},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.8385037183761597},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8328919410705566},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.8204822540283203},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.8128429651260376},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6306415796279907},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.5893464088439941},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5742952227592468},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5572049021720886},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.49581608176231384},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4801068603992462},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.46858829259872437},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4432207942008972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4326721727848053},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.296866238117218},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/s0363012904440897","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012904440897","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:1002.2373","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.2373","pdf_url":"https://arxiv.org/pdf/1002.2373","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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.393.4835","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.393.4835","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/45/59/93/PDF/dalio-ley-sicon2006.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.510.7620","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.510.7620","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.unipd.it/~dalio/DLLSiam.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.771.7917","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.771.7917","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1002.2373.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00455993v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00455993","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 Control and Optimization, 2006, 45 (1), pp.74-106. &#x27E8;10.1137/S0363012904440897&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.research.unipd.it:11577/1561628","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/1561628","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","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:arXiv.org:1002.2373","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.2373","pdf_url":"https://arxiv.org/pdf/1002.2373","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W87265819","https://openalex.org/W1483801101","https://openalex.org/W1487586009","https://openalex.org/W1505284970","https://openalex.org/W1511896630","https://openalex.org/W1513091520","https://openalex.org/W1513618711","https://openalex.org/W1515432731","https://openalex.org/W1558902221","https://openalex.org/W1567262822","https://openalex.org/W1576916260","https://openalex.org/W1580561995","https://openalex.org/W1965374374","https://openalex.org/W1976734952","https://openalex.org/W1983345526","https://openalex.org/W1986838484","https://openalex.org/W1989329198","https://openalex.org/W1998674480","https://openalex.org/W2017278207","https://openalex.org/W2032316144","https://openalex.org/W2032831203","https://openalex.org/W2045817059","https://openalex.org/W2059705075","https://openalex.org/W2064647492","https://openalex.org/W2065959526","https://openalex.org/W2076351635","https://openalex.org/W2076623791","https://openalex.org/W2077883650","https://openalex.org/W2088471261","https://openalex.org/W2093441741","https://openalex.org/W2096626244","https://openalex.org/W2141436719","https://openalex.org/W2145668749","https://openalex.org/W2178442254","https://openalex.org/W2209557103","https://openalex.org/W2292619276","https://openalex.org/W2339733371","https://openalex.org/W2407415358","https://openalex.org/W2524415518","https://openalex.org/W2749408143","https://openalex.org/W2795744704","https://openalex.org/W3021722416","https://openalex.org/W3111685920","https://openalex.org/W3150646356","https://openalex.org/W4206537305","https://openalex.org/W4212780424","https://openalex.org/W4248590282","https://openalex.org/W4299411938"],"related_works":["https://openalex.org/W4239477580","https://openalex.org/W4255265352","https://openalex.org/W2032834442","https://openalex.org/W1654696814","https://openalex.org/W3153900688","https://openalex.org/W2921905705","https://openalex.org/W4297940580","https://openalex.org/W4292330635","https://openalex.org/W4306892756","https://openalex.org/W2766998270"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,29],"prove":[4],"a":[5,35],"comparison":[6],"result":[7],"between":[8],"semicontinuous":[9],"viscosity":[10,47],"sub-":[11],"and":[12,23],"supersolutions":[13],"growing":[14],"at":[15],"most":[16],"quadratically":[17],"of":[18,34,49],"second-order":[19],"degenerate":[20],"parabolic":[21],"Hamilton--Jacobi--Bellman":[22],"Isaacs":[24],"equations.":[25],"As":[26],"an":[27],"application,":[28],"characterize":[30],"the":[31,45,50],"value":[32],"function":[33],"finite":[36],"horizon":[37],"stochastic":[38],"control":[39],"problem":[40],"with":[41],"unbounded":[42],"controls":[43],"as":[44],"unique":[46],"solution":[48],"corresponding":[51],"dynamic":[52],"programming":[53],"equation.":[54]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
