{"id":"https://openalex.org/W2962718871","doi":"https://doi.org/10.1137/16m1090338","title":"Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs","display_name":"Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2962718871","doi":"https://doi.org/10.1137/16m1090338","mag":"2962718871"},"language":"en","primary_location":{"id":"doi:10.1137/16m1090338","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1090338","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044750709","display_name":"Zhenjie Ren","orcid":"https://orcid.org/0000-0003-4656-4074"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Zhenjie Ren","raw_affiliation_strings":["CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)"],"affiliations":[{"raw_affiliation_string":"CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105990961","display_name":"Nizar Touzi","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nizar Touzi","raw_affiliation_strings":["CMAP, Ecole Polytechnique Paris,"],"affiliations":[{"raw_affiliation_string":"CMAP, Ecole Polytechnique Paris,","institution_ids":["https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100374701","display_name":"Jianfeng Zhang","orcid":"https://orcid.org/0000-0001-7922-0839"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianfeng Zhang","raw_affiliation_strings":["University of Southern California, Department of Mathematics,"],"affiliations":[{"raw_affiliation_string":"University of Southern California, Department of Mathematics,","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044750709"],"corresponding_institution_ids":["https://openalex.org/I171048554"],"apc_list":null,"apc_paid":null,"fwci":7.132,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.97749614,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"49","issue":"5","first_page":"4093","last_page":"4116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9972000122070312,"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":0.9972000122070312,"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":0.9726999998092651,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.963699996471405,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8879541158676147},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.808199405670166},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6439907550811768},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.6250705122947693},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.601697564125061},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5754992365837097},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5473187565803528},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.5371056199073792},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5152592658996582},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35209453105926514},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3303382992744446},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05553692579269409}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8879541158676147},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.808199405670166},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6439907550811768},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.6250705122947693},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.601697564125061},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5754992365837097},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5473187565803528},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.5371056199073792},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5152592658996582},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35209453105926514},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3303382992744446},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05553692579269409},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1090338","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1090338","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:HAL:hal-03909172v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03909172","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 Mathematical Analysis, 2017, 49 (5), pp.4093-4116. ⟨10.1137/16M1090338⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5049773150","display_name":null,"funder_award_id":"DMS 1413717","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G770499547","display_name":null,"funder_award_id":"1413717","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320331267","display_name":"Fondation du Risque","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1559997346","https://openalex.org/W1971594473","https://openalex.org/W2012244785","https://openalex.org/W2018706083","https://openalex.org/W2075819923","https://openalex.org/W2076091926","https://openalex.org/W2078895915","https://openalex.org/W2114974849","https://openalex.org/W2136011614","https://openalex.org/W2143365754","https://openalex.org/W2157765339","https://openalex.org/W2177195156","https://openalex.org/W2749408143","https://openalex.org/W2962853650","https://openalex.org/W2962917010","https://openalex.org/W3101566353","https://openalex.org/W3102177650","https://openalex.org/W4230022934"],"related_works":["https://openalex.org/W2971099291","https://openalex.org/W3099211396","https://openalex.org/W4317210689","https://openalex.org/W2886810076","https://openalex.org/W1484269119","https://openalex.org/W2941405134","https://openalex.org/W126524403","https://openalex.org/W2036051171","https://openalex.org/W4285445988","https://openalex.org/W2374370419"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2],"comparison":[3,82],"result":[4,21],"for":[5,41,100,105],"viscosity":[6,102],"solutions":[7],"of":[8,84,93],"(possibly":[9],"degenerate)":[10],"parabolic":[11],"fully":[12],"nonlinear":[13],"path-dependent":[14,49],"PDEs.":[15,50],"In":[16],"contrast":[17],"with":[18],"the":[19,42,54,71,81,98,101,106,109],"previous":[20],"in":[22,70],"Ekren,":[23,85],"Touzi,":[24,86],"and":[25,39,62,87,104],"Zhang":[26,88],"[Ann.":[27],"Probab.,":[28],"44":[29],"(2016),":[30],"pp.":[31],"2507--2553],":[32],"our":[33],"conditions":[34],"are":[35],"easier":[36],"to":[37,97],"check":[38],"allow":[40],"degenerate":[43],"case,":[44],"thus":[45],"including":[46],"first":[47],"order":[48],"Our":[51],"argument":[52,78],"follows":[53],"regularization":[55],"method":[56],"as":[57],"introduced":[58],"by":[59],"Jensen,":[60],"Lions,":[61],"Souganidis":[63],"[Proc.":[64],"Amer.":[65],"Math.":[66],"Soc.,":[67],"102,":[68],"(1988)]":[69],"corresponding":[72],"finite-dimensional":[73],"PDE":[74],"setting.":[75],"The":[76],"present":[77],"significantly":[79],"simplifies":[80],"proof":[83],"but":[89],"requires":[90],"an":[91],"$\\mathbb{L}^p$-type":[92],"continuity":[94],"(with":[95],"respect":[96],"path)":[99],"semisolutions":[103],"nonlinearity":[107],"defining":[108],"equation.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}