{"id":"https://openalex.org/W4240752643","doi":"https://doi.org/10.1137/s0036141098338843","title":"A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space","display_name":"A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W4240752643","doi":"https://doi.org/10.1137/s0036141098338843"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141098338843","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141098338843","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/A5054561472","display_name":"\u041d. \u0412. \u041a\u0440\u044b\u043b\u043e\u0432","orcid":"https://orcid.org/0000-0002-2068-0432"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. V. Krylov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074998820","display_name":"Sergey V. Lototsky","orcid":"https://orcid.org/0000-0003-3260-1348"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. V. Lototsky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0716,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.86881419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"1","first_page":"19","last_page":"33"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9969000220298767,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.9067723751068115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8933260440826416},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6543794274330139},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6066156625747681},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5790454745292664},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.4581434428691864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35555657744407654},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.33593758940696716},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08800184726715088},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05057114362716675}],"concepts":[{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.9067723751068115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8933260440826416},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6543794274330139},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6066156625747681},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5790454745292664},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.4581434428691864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35555657744407654},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33593758940696716},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08800184726715088},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05057114362716675},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/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/s0036141098338843","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141098338843","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:CiteSeerX.psu:10.1.1.374.468","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.374.468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-bcf.usc.edu/~lototsky/KrLt_hl.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2019745466","https://openalex.org/W2039634154","https://openalex.org/W2059091656","https://openalex.org/W2059278953","https://openalex.org/W4249779810"],"related_works":["https://openalex.org/W4299978068","https://openalex.org/W2950745223","https://openalex.org/W2164189677","https://openalex.org/W4301407218","https://openalex.org/W4388311156","https://openalex.org/W4296771954","https://openalex.org/W2963735960","https://openalex.org/W1869870390","https://openalex.org/W2811033119","https://openalex.org/W2013426140"],"abstract_inverted_index":{"Equations":[0],"of":[1,18],"the":[2,35],"form":[3],"$du=(a^{ij}u_{x^{i}x^{j}}":[4],"+D_{i}f^{i})\\,dt+\\sum_{k}(\\sigma^{ik}u_{x^{i}}":[5],"+g^{k})\\,dw^{k}_{t}$":[6],"are":[7],"considered":[8],"for":[9],"t":[10],">":[11],"0":[12],"and":[13],"$x\\in\\bR^{d}_{+}$.":[14],"The":[15],"unique":[16],"solvability":[17],"these":[19],"equations":[20],"is":[21],"proved":[22],"in":[23],"weighted":[24],"Sobolev":[25],"spaces":[26],"with":[27],"fractional":[28],"positive":[29],"or":[30],"negative":[31],"derivatives,":[32],"summable":[33],"to":[34],"power":[36],"$p\\in[2,\\infty)$.":[37]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}