{"id":"https://openalex.org/W1978796191","doi":"https://doi.org/10.1070/sm2014v205n11abeh004428","title":"Polynomial solutions of the Monge-Amp\u00e8re equation","display_name":"Polynomial solutions of the Monge-Amp\u00e8re equation","publication_year":2014,"publication_date":"2014-11-30","ids":{"openalex":"https://openalex.org/W1978796191","doi":"https://doi.org/10.1070/sm2014v205n11abeh004428","mag":"1978796191"},"language":"en","primary_location":{"id":"doi:10.1070/sm2014v205n11abeh004428","doi":"https://doi.org/10.1070/sm2014v205n11abeh004428","is_oa":false,"landing_page_url":"https://doi.org/10.1070/sm2014v205n11abeh004428","pdf_url":null,"source":{"id":"https://openalex.org/S89900327","display_name":"Sbornik Mathematics","issn_l":"1064-5616","issn":["1064-5616","1468-4802"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sbornik: Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5017792003","display_name":"Yu. A. Aminov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yu A Aminov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017792003"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"205","issue":"11","first_page":"1529","last_page":"1563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.4528999924659729,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.4528999924659729,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.12620000541210175,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.07039999961853027,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/monge-ampere-equation","display_name":"Monge-Amp\u00e8re equation","score":0.996999979019165},{"id":"https://openalex.org/keywords/polynomial-solutions","display_name":"polynomial solutions","score":0.9980000257492065},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.8399999737739563},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.5989999771118164},{"id":"https://openalex.org/keywords/necessary-and-sufficient-conditions","display_name":"necessary and sufficient conditions","score":0.8309999704360962},{"id":"https://openalex.org/keywords/approximation-theorems","display_name":"approximation theorems","score":0.7950000166893005},{"id":"https://openalex.org/keywords/second-order-partial-differential-equations","display_name":"second-order partial differential equations","score":0.5580000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8697217702865601},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6002512574195862},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43900924921035767},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4266766309738159},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35947591066360474},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23902848362922668}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1070/sm2014v205n11abeh004428","doi":"https://doi.org/10.1070/sm2014v205n11abeh004428","is_oa":false,"landing_page_url":"https://doi.org/10.1070/sm2014v205n11abeh004428","pdf_url":null,"source":{"id":"https://openalex.org/S89900327","display_name":"Sbornik Mathematics","issn_l":"1064-5616","issn":["1064-5616","1468-4802"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sbornik: Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W633227097","https://openalex.org/W1971102216","https://openalex.org/W1989531777","https://openalex.org/W2010096691","https://openalex.org/W2073288507","https://openalex.org/W2086847722","https://openalex.org/W2093716197","https://openalex.org/W2321666324","https://openalex.org/W4242717346","https://openalex.org/W4247210210","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W7131940281","https://openalex.org/W2981097551","https://openalex.org/W2010096691","https://openalex.org/W4390762248","https://openalex.org/W2785577233","https://openalex.org/W1982335787","https://openalex.org/W2958408431","https://openalex.org/W2003677132","https://openalex.org/W2964036503","https://openalex.org/W2885406661"],"abstract_inverted_index":{"The":[0],"question":[1],"of":[2,5,36,46,76,89,92,104],"the":[3,9,20,37,61,74,77,87,102],"existence":[4,88],"polynomial":[6,35,57,69,90],"solutions":[7,91,106],"to":[8,95],"Monge-Ampere":[10],"equation":[11],"z{sub":[12],"xx}z{sub":[13],"yy}\u2212z{sub":[14],"xy}{sup":[15],"2}=f(x,y)":[16],"is":[17,24,28,33,41,67,71,80,112],"considered":[18],"in":[19,73],"case":[21],"when":[22],"f(x,y)":[23],"a":[25,34,51,64],"polynomial.":[26],"It":[27],"proved":[29],"that":[30],"if":[31],"f":[32],"second":[38],"degree,":[39],"which":[40,66],"positive":[42,52],"for":[43,86,101],"all":[44],"values":[45],"its":[47],"arguments":[48],"and":[49,83,99],"has":[50],"squared":[53],"part,":[54],"then":[55],"no":[56],"solution":[58,65],"exists.":[59],"On":[60],"other":[62],"hand,":[63],"not":[68],"but":[70],"analytic":[72],"whole":[75],"x,":[78],"y-plane":[79],"produced.":[81],"Necessary":[82],"sufficient":[84],"conditions":[85],"degree":[93],"up":[94],"4":[96],"are":[97,107],"found":[98],"methods":[100],"construction":[103],"such":[105],"indicated.":[108],"An":[109],"approximation":[110],"theorem":[111],"proved.":[113],"Bibliography:":[114],"10":[115],"titles.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}