{"id":"https://openalex.org/W2963685923","doi":"https://doi.org/10.1137/17m1160409","title":"Rates of Convergence in $W^2_p$-Norm for the Monge--Amp\u00e8re Equation","display_name":"Rates of Convergence in $W^2_p$-Norm for the Monge--Amp\u00e8re Equation","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963685923","doi":"https://doi.org/10.1137/17m1160409","mag":"2963685923"},"language":"en","primary_location":{"id":"doi:10.1137/17m1160409","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160409","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical 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/A5039552338","display_name":"Michael Neilan","orcid":"https://orcid.org/0000-0002-1564-1041"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Neilan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029100440","display_name":"Wujun Zhang","orcid":"https://orcid.org/0000-0003-4066-8534"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wujun Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039552338"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2767,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.88568165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"56","issue":"5","first_page":"3099","last_page":"3120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9994000196456909,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9994000196456909,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9965999722480774,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9847000241279602,"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/mathematics","display_name":"Mathematics","score":0.871683657169342},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5444787740707397},{"id":"https://openalex.org/keywords/monge\u2013amp\u00e8re-equation","display_name":"Monge\u2013Amp\u00e8re equation","score":0.5099364519119263},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36843743920326233}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.871683657169342},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5444787740707397},{"id":"https://openalex.org/C2777808208","wikidata":"https://www.wikidata.org/wiki/Q1552291","display_name":"Monge\u2013Amp\u00e8re equation","level":2,"score":0.5099364519119263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36843743920326233},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1160409","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160409","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2021430723","display_name":null,"funder_award_id":"DMS-1818861","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3952655055","display_name":null,"funder_award_id":"DMS-1719829","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4848625425","display_name":null,"funder_award_id":"DMS-1541585","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/F4320312581","display_name":"Rutgers, The State University of New Jersey","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1549932963","https://openalex.org/W1967250370","https://openalex.org/W1994521023","https://openalex.org/W2009553465","https://openalex.org/W2011600769","https://openalex.org/W2019270511","https://openalex.org/W2036759661","https://openalex.org/W2049106345","https://openalex.org/W2054762334","https://openalex.org/W2084358734","https://openalex.org/W2084587134","https://openalex.org/W2086803896","https://openalex.org/W2116442609","https://openalex.org/W2155324103","https://openalex.org/W2177195156","https://openalex.org/W2280333052","https://openalex.org/W2313087217","https://openalex.org/W2330394843","https://openalex.org/W2335594173","https://openalex.org/W2963149381","https://openalex.org/W2963243433"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2028134003","https://openalex.org/W2963430243"],"abstract_inverted_index":{"We":[0],"develop":[1],"discrete":[2,20],"$W^2_p$-norm":[3],"error":[4,68],"estimates":[5,22],"for":[6],"the":[7,12,26,44,47,50,56,59,67,105,111,115,129],"Oliker--Prussner":[8],"method":[9],"applied":[10],"to":[11],"Monge--Amp\u00e8re":[13],"equation.":[14],"This":[15],"is":[16,53,99,131],"obtained":[17],"by":[18,55],"extending":[19],"Alexandroff":[21],"and":[23,84,104,114,126],"showing":[24],"that":[25,43,66,128],"contact":[27,51],"set":[28,52],"of":[29,46,49,58],"a":[30,100],"nodal":[31],"function":[32],"contains":[33],"information":[34],"on":[35,109],"its":[36],"second-order":[37],"difference.":[38],"In":[39],"addition,":[40],"we":[41,64],"show":[42,65],"size":[45],"complement":[48],"controlled":[54],"consistency":[57],"method.":[60],"Combining":[61],"both":[62],"observations,":[63],"estimate":[69,130],"$\\|":[70],"u":[71],"-":[72],"u_h":[73],"\\|_{W^2_{f,p}}":[74],"(\\mathcal{N}^I_h)$":[75],"converges":[76,85],"in":[77,86,122,133],"order":[78,87],"$O(h^{1/p})$":[79],"if":[80,93],"$p":[81,94],">":[82],"d$":[83],"$O(h^{1/d}":[88],"\\ln":[89],"(\\frac":[90],"1":[91],"h)^{1/d})$":[92],"\\leq":[95],"d$,":[96],"where":[97],"$\\|\\cdot\\|_{W^2_{f,p}(\\mathcal{N}^I_h)}$":[98],"weighted":[101],"$W^2_p$-type":[102],"norm,":[103],"constant":[106,116],"$C>0$":[107],"depends":[108],"$\\|{u}\\|_{C^{3,1}(\\bar\\Omega)}$,":[110],"dimension":[112],"$d$,":[113],"$p$.":[117],"Numerical":[118],"examples":[119],"are":[120],"given":[121],"two":[123],"space":[124],"dimensions":[125],"confirm":[127],"sharp":[132],"several":[134],"cases.":[135]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
