{"id":"https://openalex.org/W2087014689","doi":"https://doi.org/10.1137/130950549","title":"A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type","display_name":"A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2087014689","doi":"https://doi.org/10.1137/130950549","mag":"2087014689"},"language":"en","primary_location":{"id":"doi:10.1137/130950549","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130950549","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1401.6369","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057727807","display_name":"Arnaud Debussche","orcid":"https://orcid.org/0000-0002-8558-7976"},"institutions":[{"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":true,"raw_author_name":"Arnaud Debussche","raw_affiliation_strings":["IPSO - Invariant Preserving SOlvers (France)","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)"],"affiliations":[{"raw_affiliation_string":"IPSO - Invariant Preserving SOlvers (France)","institution_ids":[]},{"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"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021346231","display_name":"Sylvain De Moor","orcid":null},"institutions":[{"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":"Sylvain de Moor","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)"],"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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007048442","display_name":"Martina Hofmanov\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]},{"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":["DE","FR"],"is_corresponding":false,"raw_author_name":"Martina Hofmanov\u00e1","raw_affiliation_strings":["TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Germany)","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)"],"affiliations":[{"raw_affiliation_string":"TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Germany)","institution_ids":["https://openalex.org/I4577782"]},{"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"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057727807"],"corresponding_institution_ids":["https://openalex.org/I4210161663"],"apc_list":null,"apc_paid":null,"fwci":13.3124,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.98793949,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"47","issue":"2","first_page":"1590","last_page":"1614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9972000122070312,"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":0.9972000122070312,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9882000088691711,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9851999878883362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9161573052406311},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.7580403685569763},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.6638759970664978},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6235230565071106},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.6143198609352112},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6106529831886292},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5811688899993896},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4907701909542084},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.48334214091300964},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4432946741580963},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4294370710849762},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39856258034706116}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9161573052406311},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.7580403685569763},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.6638759970664978},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6235230565071106},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.6143198609352112},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6106529831886292},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5811688899993896},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4907701909542084},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.48334214091300964},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4432946741580963},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4294370710849762},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39856258034706116},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130950549","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130950549","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:arXiv.org:1401.6369","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.6369","pdf_url":"https://arxiv.org/pdf/1401.6369","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-00935892v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00935892","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2015, 47 (2), pp.1590-1614. &#x27E8;10.1137/130950549&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.6369","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.6369","pdf_url":"https://arxiv.org/pdf/1401.6369","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W35304917","https://openalex.org/W162854683","https://openalex.org/W222993076","https://openalex.org/W1542004730","https://openalex.org/W1568807173","https://openalex.org/W1594554612","https://openalex.org/W1596333210","https://openalex.org/W1602967628","https://openalex.org/W1794301351","https://openalex.org/W1807107269","https://openalex.org/W1972342108","https://openalex.org/W1975879354","https://openalex.org/W1999691346","https://openalex.org/W2024809264","https://openalex.org/W2041714615","https://openalex.org/W2043496299","https://openalex.org/W2077507254","https://openalex.org/W2088636834","https://openalex.org/W2097536962","https://openalex.org/W2134604477","https://openalex.org/W2136811813","https://openalex.org/W2140084118","https://openalex.org/W2369386221","https://openalex.org/W2733824364","https://openalex.org/W2964124635","https://openalex.org/W3105683009"],"related_works":["https://openalex.org/W2123186262","https://openalex.org/W1972240278","https://openalex.org/W620239920","https://openalex.org/W109055908","https://openalex.org/W2735510078","https://openalex.org/W1546584948","https://openalex.org/W184885699","https://openalex.org/W2950472683","https://openalex.org/W94839203","https://openalex.org/W302182746"],"abstract_inverted_index":{"We":[0,24],"consider":[1],"a":[2,12,21,34,84,102],"nondegenerate":[3],"quasilinear":[4],"parabolic":[5,86,104],"stochastic":[6,125],"partial":[7],"differential":[8],"equation":[9],"(SPDE)":[10],"with":[11,88,106],"uniformly":[13],"elliptic":[14],"diffusion":[15],"matrix.":[16],"It":[17],"is":[18,52,63,74],"driven":[19],"by":[20,117],"nonlinear":[22],"noise.":[23],"study":[25],"regularity":[26,113],"properties":[27],"of":[28,69,79,121],"its":[29],"weak":[30,50],"solution":[31,51,73],"satisfying":[32],"classical":[33],"priori":[35],"estimates.":[36],"In":[37],"particular,":[38],"we":[39],"determine":[40],"conditions":[41],"on":[42,65],"coefficients":[43],"and":[44,57,127],"initial":[45],"data":[46],"under":[47],"which":[48],"the":[49,72,77,89,94,99,111],"H\u00f6lder":[53],"continuous":[54],"in":[55],"time":[56],"possesses":[58],"spatial":[59],"regularity.":[60],"Our":[61],"proof":[62],"based":[64],"an":[66],"efficient":[67],"method":[68],"increasing":[70],"regularity:":[71],"rewritten":[75],"as":[76,93],"sum":[78],"two":[80],"processes,":[81],"one":[82],"solves":[83,101],"linear":[85,103],"SPDE":[87],"same":[90],"noise":[91],"term":[92],"original":[95],"model":[96],"problem":[97],"whereas":[98],"other":[100],"PDE":[105],"random":[107],"coefficients.":[108],"This":[109],"way,":[110],"required":[112],"can":[114],"be":[115],"achieved":[116],"repeatedly":[118],"making":[119],"use":[120],"known":[122],"techniques":[123],"for":[124],"convolutions":[126],"deterministic":[128],"PDEs.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
