{"id":"https://openalex.org/W7203502269","doi":"https://doi.org/10.48550/arxiv.2608.13380","title":"Unbounded variation solutions for uniformly elliptic equations in nondivergence form in dimension three","display_name":"Unbounded variation solutions for uniformly elliptic equations in nondivergence form in dimension three","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7203502269","doi":"https://doi.org/10.48550/arxiv.2608.13380"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.13380","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13380","pdf_url":"https://arxiv.org/pdf/2608.13380","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.13380","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027907644","display_name":"Nam Q. Le","orcid":"https://orcid.org/0000-0001-6847-7305","observed_orcids":["https://orcid.org/0000-0001-6847-7305"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Le, Nam Q.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147149865","display_name":"Qi Sun","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Qi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134462288","display_name":"Hung V. Tran","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tran, Hung V.","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":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9868000149726868,"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":0.9868000149726868,"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":0.004800000227987766,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.0019000000320374966,"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/uniformly-elliptic-equations","display_name":"uniformly elliptic equations","score":0.953000009059906},{"id":"https://openalex.org/keywords/non-divergence-form","display_name":"non-divergence form","score":0.9890000224113464},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.5649999976158142},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.6690000295639038},{"id":"https://openalex.org/keywords/functions-of-bounded-variation","display_name":"functions of bounded variation","score":0.37299999594688416},{"id":"https://openalex.org/keywords/regularity-of-solutions","display_name":"regularity of solutions","score":0.4749999940395355}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8282999992370605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.7032999992370605},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6992999911308289},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6069999933242798},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4715000092983246},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.44699999690055847},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4431000053882599},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.39750000834465027},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3190000057220459},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2913999855518341},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.28870001435279846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.13380","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13380","pdf_url":"https://arxiv.org/pdf/2608.13380","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.13380","doi":"https://doi.org/10.48550/arxiv.2608.13380","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.13380","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.13380","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13380","pdf_url":"https://arxiv.org/pdf/2608.13380","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3471374583","display_name":"Singular Higher-order Linearized Monge-Amp\u00e8re Type Equations with Drifts","funder_award_id":"2452320","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3662062301","display_name":"Viscosity Solutions: Beyond the Wellposedness Theory","funder_award_id":"2348305","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203502269.pdf","grobid_xml":"https://content.openalex.org/works/W7203502269.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4409361384","https://openalex.org/W1969454786","https://openalex.org/W2325290469","https://openalex.org/W2000760919","https://openalex.org/W1630057127","https://openalex.org/W603286626","https://openalex.org/W7008709083","https://openalex.org/W2012867970","https://openalex.org/W2060911541","https://openalex.org/W1974417402"],"abstract_inverted_index":{"For":[0],"each":[1],"nonnegative":[2],"integer":[3],"$m$,":[4],"we":[5],"construct":[6],"smooth":[7,27],"symmetric":[8],"$3\\times":[9],"3$":[10],"coefficient":[11,107],"matrices":[12],"$A_m$":[13],"satisfying":[14],"the":[15,26,80,115],"fixed":[16],"ellipticity":[17,64],"bound":[18],"\\[":[19,36,50],"I\\leq":[20],"A_m\\leq":[21],"2^{81}I":[22],"\\]":[23,42,53],"for":[24,74,102],"which":[25],"solutions":[28],"of":[29,114],"uniformly":[30,96,105],"elliptic":[31,106],"equations":[32],"in":[33,65,79],"nondivergence":[34],"form":[35],"\\text{tr}(A_m(x)D^2":[37],"u_m)=A_m(x):D^2u_m=0\\qquad\\text{in":[38],"}B_2\\subset":[39],"{\\mathbb":[40],"R}^3":[41],"have":[43],"common":[44],"Dirichlet":[45],"data,":[46],"satisfy":[47],"$\\|u_m\\|_{L^\\infty(B_2)}\\leq1$,":[48],"but":[49],"\\lim_{m\\to":[51],"\\infty}\\|Du_m\\|_{L^1(B_1)}=\\infty.":[52],"Thus,":[54],"there":[55],"is":[56],"no":[57,70],"interior":[58],"$W^{1,1}$":[59],"estimate":[60,73],"depending":[61],"only":[62],"on":[63],"dimension":[66],"three,":[67],"and":[68,89],"consequently":[69],"such":[71],"$W^{1,p}$":[72],"any":[75],"$p\\geq1$.":[76],"This":[77],"resolves":[78],"negative":[81],"an":[82,111],"open":[83],"question":[84],"raised":[85],"by":[86],"Nadirashvili,":[87],"Tkachev,":[88],"Vl\u0103du\u0163.":[90],"The":[91],"construction":[92],"also":[93],"gives":[94],"a":[95,103],"convergent":[97],"limit":[98,113],"$u\\notin":[99],"\\text{BV}_{\\rm":[100],"loc}(B_1)$":[101],"measurable":[104],"matrix":[108],"obtained":[109],"as":[110],"$L^1$":[112],"$A_m$.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-15T00:00:00"}
