{"id":"https://openalex.org/W7223033770","doi":"https://doi.org/10.48550/arxiv.2610.25375","title":"A dual variational principle for the Moser-Trudinger inequality: existence, uniqueness and stability of extremals","display_name":"A dual variational principle for the Moser-Trudinger inequality: existence, uniqueness and stability of extremals","publication_year":2026,"publication_date":"2026-10-18","ids":{"openalex":"https://openalex.org/W7223033770","doi":"https://doi.org/10.48550/arxiv.2610.25375"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.25375","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25375","pdf_url":"https://arxiv.org/pdf/2610.25375","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/2610.25375","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159100671","display_name":"Jungang Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Jungang","raw_affiliation_strings":["University of Science and Technology of China , Hefei 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China , Hefei 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159158928","display_name":"Wen Sun","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sun, Wen","raw_affiliation_strings":["University of Science and Technology of China , Hefei 230026 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China , Hefei 230026 , China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9951000213623047,"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":0.9951000213623047,"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/T11564","display_name":"Mathematical Inequalities and Applications","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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0008999999845400453,"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/trudinger-moser-inequality","display_name":"Trudinger-Moser inequality","score":1.0},{"id":"https://openalex.org/keywords/sharp-constants","display_name":"sharp constants","score":0.46399998664855957},{"id":"https://openalex.org/keywords/extremal-functions","display_name":"extremal functions","score":0.8420000076293945},{"id":"https://openalex.org/keywords/nondegeneracy","display_name":"nondegeneracy","score":0.8539999723434448},{"id":"https://openalex.org/keywords/stability-estimates","display_name":"stability estimates","score":0.7269999980926514},{"id":"https://openalex.org/keywords/gibbs-variational-principle","display_name":"Gibbs variational principle","score":0.8410000205039978},{"id":"https://openalex.org/keywords/legendre-transform","display_name":"Legendre transform","score":0.824999988079071},{"id":"https://openalex.org/keywords/threshold-concentration","display_name":"threshold concentration","score":0.652999997138977},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.6190000176429749},{"id":"https://openalex.org/keywords/quantitative-stability","display_name":"quantitative stability","score":0.47999998927116394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8690999746322632},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6687999963760376},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6137999892234802},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6008999943733215},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5992000102996826},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5884000062942505},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4878999888896942},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46320000290870667},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3749000132083893},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.37369999289512634},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34049999713897705},{"id":"https://openalex.org/C116594300","wikidata":"https://www.wikidata.org/wiki/Q908652","display_name":"Legendre transformation","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.25375","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25375","pdf_url":"https://arxiv.org/pdf/2610.25375","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.2610.25375","doi":"https://doi.org/10.48550/arxiv.2610.25375","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25375","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:2610.25375","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25375","pdf_url":"https://arxiv.org/pdf/2610.25375","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/G6717701567","display_name":null,"funder_award_id":"12571127","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6854096065","display_name":null,"funder_award_id":"12401171","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223033770.pdf","grobid_xml":"https://content.openalex.org/works/W7223033770.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7160447602","https://openalex.org/W7214040853"],"related_works":["https://openalex.org/W2516575429","https://openalex.org/W2950259538","https://openalex.org/W2804421333","https://openalex.org/W4212840149","https://openalex.org/W2064213279","https://openalex.org/W2817097260","https://openalex.org/W1692219692","https://openalex.org/W2800147902","https://openalex.org/W3095500473","https://openalex.org/W7099077836"],"abstract_inverted_index":{"For":[0,79],"$p>1$,":[1],"with":[2,83,144],"$p'=p/(p-1)$,":[3],"we":[4,81,131],"prove":[5],"the":[6,20,23,31,39,46,58,67,88,97,100,150],"sharp":[7],"dual":[8,35,55,90],"inequality":[9,102],"$$":[10,16,133,139],"\\int_0^1-\\log\\left(1-\\frac{\\left|\\int_0^xf(y)":[11],"dy\\right|^{p'}}{x}\\right)":[12],"dx\\leq\\mathsf{K}_p,":[13],"\\qquad":[14],"\\|f\\|_{L^p(0,1)}\\leq1,":[15],"where":[17],"$\\mathsf{K}_p$":[18],"is":[19,51,71,92,107,125,153],"logarithm":[21],"of":[22,30,57,61,99,114,118,160],"optimal":[24],"value":[25],"in":[26,76],"Moser's":[27],"one-dimensional":[28],"formulation":[29],"Moser-Trudinger":[32,101],"inequality.":[33,78],"The":[34,121],"functional":[36],"follows":[37],"from":[38],"Gibbs":[40],"variational":[41],"principle,":[42],"monotone":[43],"transport":[44],"and":[45,64,94,117,149],"Legendre":[47],"transform.":[48],"Its":[49],"supremum":[50],"attained,":[52],"giving":[53,155],"a":[54,104,156],"proof":[56],"existence":[59],"theorems":[60],"Carleson-Chang":[62],"(1986)":[63],"Hudson-Leckband":[65],"(2002);":[66],"classical":[68],"concentration":[69],"threshold":[70],"realized":[72],"by":[73],"equality":[74],"cases":[75],"Hoelder's":[77],"$p=2$":[80],"prove,":[82],"rigorous":[84],"computer-assisted":[85],"estimates,":[86],"that":[87],"nonnegative":[89],"maximizer":[91],"unique":[93,108],"nondegenerate.":[95],"Hence":[96],"extremal":[98,123],"on":[103],"disk":[105],"$D$":[106],"up":[109],"to":[110],"sign,":[111],"confirming":[112],"conjectures":[113],"Adimurthi-Karthik-Giacomoni":[115],"(2016)":[116],"Chen-Lu-Xue-Zhu":[119],"(2026).":[120],"positive":[122],"$u_*$":[124],"nondegenerate,":[126],"and,":[127],"writing":[128],"$\\mathcal{M}_D(u)=|D|^{-1}\\int_De^{4\u03c0u^2}":[129],"dx$,":[130],"obtain":[132],"\\mathcal{M}_D(u_*)-\\mathcal{M}_D(u)":[134],"\\geq":[135],"c":[136],"\\min_{\\pm}\\|\\nabla(u\\mp":[137],"u_*)\\|_{L^2(D)}^2":[138],"for":[140],"all":[141],"$u\\in":[142],"H_0^1(D)$":[143],"$\\|\\nabla":[145],"u\\|_{L^2(D)}\\leq1$.":[146],"Here":[147],"$c>0$,":[148],"exponent":[151],"two":[152],"optimal,":[154],"quantitative":[157],"stability":[158],"theorem":[159],"Bianchi-Egnell":[161],"type.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}