{"id":"https://openalex.org/W2559172583","doi":"https://doi.org/10.1155/2016/4649150","title":"Uniqueness of Solutions to a Nonlinear Elliptic Hessian Equation","display_name":"Uniqueness of Solutions to a Nonlinear Elliptic Hessian Equation","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2559172583","doi":"https://doi.org/10.1155/2016/4649150","mag":"2559172583"},"language":"lv","primary_location":{"id":"doi:10.1155/2016/4649150","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2016/4649150","pdf_url":"http://downloads.hindawi.com/journals/jam/2016/4649150.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/jam/2016/4649150.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057208745","display_name":"Siyuan Li","orcid":"https://orcid.org/0000-0001-5014-9979"},"institutions":[{"id":"https://openalex.org/I204824540","display_name":"University of Wollongong","ror":"https://ror.org/00jtmb277","country_code":"AU","type":"education","lineage":["https://openalex.org/I204824540"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Siyuan Li","raw_affiliation_strings":["School of Mathematics and Applied Statistics, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW 2522, Australia"],"raw_orcid":"https://orcid.org/0000-0001-5014-9979","affiliations":[{"raw_affiliation_string":"School of Mathematics and Applied Statistics, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW 2522, Australia","institution_ids":["https://openalex.org/I204824540"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057208745"],"corresponding_institution_ids":["https://openalex.org/I204824540"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16095339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2016","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9990000128746033,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.855232834815979},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8189566135406494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5499356985092163},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5025990009307861},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4016836881637573},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3422938883304596},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13741430640220642}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.855232834815979},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8189566135406494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5499356985092163},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5025990009307861},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4016836881637573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3422938883304596},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13741430640220642},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1155/2016/4649150","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2016/4649150","pdf_url":"http://downloads.hindawi.com/journals/jam/2016/4649150.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ro.uow.edu.au:eispapers-7391","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/eispapers/6361","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty of Engineering and Information Sciences - Papers: Part A","raw_type":"article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1485313385","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1485313385","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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:RePEc:hin:jnljam:4649150","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2016/4649150.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:c458c788b6344238ac1a2ece9a41169e","is_oa":false,"landing_page_url":"https://doaj.org/article/c458c788b6344238ac1a2ece9a41169e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2016 (2016)","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/27762900","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"}],"best_oa_location":{"id":"doi:10.1155/2016/4649150","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2016/4649150","pdf_url":"http://downloads.hindawi.com/journals/jam/2016/4649150.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2559172583.pdf","grobid_xml":"https://content.openalex.org/works/W2559172583.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W652391911","https://openalex.org/W1559046372","https://openalex.org/W1988420172","https://openalex.org/W2012840725","https://openalex.org/W2055820640","https://openalex.org/W2058729414","https://openalex.org/W2082611711","https://openalex.org/W2092129230","https://openalex.org/W2281671182"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W1996936972","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2076935033","https://openalex.org/W781002220","https://openalex.org/W4298171390","https://openalex.org/W2054913407","https://openalex.org/W2790537288"],"abstract_inverted_index":{"Through":[0],"an":[1],"Alexandrov-Fenchel":[2],"inequality,":[3],"we":[4,11],"establish":[5],"the":[6,13],"general":[7],"Brunn-Minkowski":[8],"inequality.":[9],"Then":[10],"obtain":[12],"uniqueness":[14],"of":[15],"solutions":[16],"to":[17],"a":[18],"nonlinear":[19],"elliptic":[20],"Hessian":[21],"equation":[22],"on<mml:math":[23],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[24],"id=\"M1\"><mml:mrow><mml:msup><mml:mrow><mml:mi":[25],"mathvariant=\"double-struck\">S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>.":[26]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
