{"id":"https://openalex.org/W7119108800","doi":"https://doi.org/10.1137/25m1751001","title":"Partial Regularity of Semiconvex Viscosity Supersolutions to Fully Nonlinear Elliptic HJB Equations and Applications to Stochastic Control","display_name":"Partial Regularity of Semiconvex Viscosity Supersolutions to Fully Nonlinear Elliptic HJB Equations and Applications to Stochastic Control","publication_year":2026,"publication_date":"2026-01-07","ids":{"openalex":"https://openalex.org/W7119108800","doi":"https://doi.org/10.1137/25m1751001"},"language":"en","primary_location":{"id":"doi:10.1137/25m1751001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1751001","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://cris.unibo.it/bitstream/11585/1035760/3/2025-01-19_mr_Federico-Ferrari-Rosestolato-December24.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063340450","display_name":"Salvatore Federico","orcid":"https://orcid.org/0000-0001-5066-2203"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Salvatore Federico","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020814759","display_name":"Giorgio Ferrari","orcid":"https://orcid.org/0000-0002-2125-3301"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giorgio Ferrari","raw_affiliation_strings":["Center for Mathematical Economics (IMW), Bielefeld University, Universit\u00e4tsstrasse 25, 33615 Bielefeld, Germany"],"affiliations":[{"raw_affiliation_string":"Center for Mathematical Economics (IMW), Bielefeld University, Universit\u00e4tsstrasse 25, 33615 Bielefeld, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026739567","display_name":"Mauro Rosestolato","orcid":"https://orcid.org/0000-0002-0049-0092"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mauro Rosestolato","raw_affiliation_strings":["Dipartimento di Economia, Universit\u00e0 di Genova, Via F. Vivaldi 5, 16126 Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Economia, Universit\u00e0 di Genova, Via F. Vivaldi 5, 16126 Genova, Italy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063340450"],"corresponding_institution_ids":["https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06889149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"1","first_page":"149","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.6837999820709229,"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":0.6837999820709229,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.07779999822378159,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.034699998795986176,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.7688000202178955},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.711899995803833},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6104000210762024},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5515999794006348},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5300999879837036},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5162000060081482},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.5097000002861023},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.47450000047683716},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42010000348091125}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8317000269889832},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.7688000202178955},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.711899995803833},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6104000210762024},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5515999794006348},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5300999879837036},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5162000060081482},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.5097000002861023},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48989999294281006},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.47450000047683716},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42010000348091125},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.41100001335144043},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4009000062942505},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.4002000093460083},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.37389999628067017},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3594000041484833},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C63331456","wikidata":"https://www.wikidata.org/wiki/Q1308570","display_name":"Stochastic calculus","level":4,"score":0.30570000410079956},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C99888217","wikidata":"https://www.wikidata.org/wiki/Q1288707","display_name":"Stopping time","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/25m1751001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1751001","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:cris.unibo.it:11585/1035760","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/1035760","pdf_url":"https://cris.unibo.it/bitstream/11585/1035760/3/2025-01-19_mr_Federico-Ferrari-Rosestolato-December24.pdf","source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:cris.unibo.it:11585/1035760","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/1035760","pdf_url":"https://cris.unibo.it/bitstream/11585/1035760/3/2025-01-19_mr_Federico-Ferrari-Rosestolato-December24.pdf","source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7119108800.pdf","grobid_xml":"https://content.openalex.org/works/W7119108800.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W592962635","https://openalex.org/W1494380031","https://openalex.org/W1507126399","https://openalex.org/W1986314707","https://openalex.org/W1990728587","https://openalex.org/W1994791309","https://openalex.org/W2032316144","https://openalex.org/W2042086201","https://openalex.org/W2047359202","https://openalex.org/W2158969568","https://openalex.org/W2600020608","https://openalex.org/W2742332334","https://openalex.org/W2810814059","https://openalex.org/W2925136200","https://openalex.org/W2964191202","https://openalex.org/W3111938011","https://openalex.org/W3112728604","https://openalex.org/W3138035360","https://openalex.org/W4213199439","https://openalex.org/W4242473853","https://openalex.org/W4249667877","https://openalex.org/W4312059531"],"related_works":[],"abstract_inverted_index":{"In":[0,59],"this":[1],"note,":[2],"we":[3],"show":[4],"that":[5],"a":[6,12,46,67,80],"locally":[7],"semiconvex":[8],"viscosity":[9],"supersolution":[10],"of":[11,29,66,79],"possibly":[13],"degenerate":[14],"fully":[15],"nonlinear":[16],"elliptic":[17],"Hamilton\u2013Jacobi\u2013Bellman":[18],"equation":[19],"is":[20,95,100],"differentiable":[21],"along":[22],"the":[23,27,30,35,64,73,77,92,97],"directions":[24],"spanned":[25],"by":[26],"range":[28],"coefficient":[31],"matrix":[32],"associated":[33],"with":[34,45],"second-order":[36,93],"term.":[37],"The":[38],"proof":[39],"combines":[40],"tools":[41],"from":[42],"convex":[43],"analysis":[44],"contradiction":[47],"argument.":[48],"This":[49],"result":[50],"has":[51],"significant":[52],"implications":[53],"for":[54],"stationary":[55],"stochastic":[56],"control":[57,71,89],"problems.":[58],"drift-control":[60],"problems,":[61,90],"it":[62],"enables":[63],"construction":[65],"candidate":[68],"optimal":[69,85],"feedback":[70],"in":[72,84],"classical":[74],"sense":[75],"and":[76,87],"establishment":[78],"verification":[81],"theorem.":[82],"Moreover,":[83],"stopping":[86],"impulse":[88],"when":[91],"term":[94],"nondegenerate,":[96],"value":[98],"function":[99],"shown":[101],"to":[102],"be":[103],"continuously":[104],"differentiable.":[105]},"counts_by_year":[],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2026-01-08T00:00:00"}