{"id":"https://openalex.org/W7203487615","doi":"https://doi.org/10.48550/arxiv.2608.13443","title":"Fundamental Gaps for the Dirichlet p-Laplacian on Convex Domains","display_name":"Fundamental Gaps for the Dirichlet p-Laplacian on Convex Domains","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7203487615","doi":"https://doi.org/10.48550/arxiv.2608.13443"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.13443","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13443","pdf_url":"https://arxiv.org/pdf/2608.13443","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.13443","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159972972","display_name":"Rui Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Rui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091049001","display_name":"Daniel Hauer","orcid":"https://orcid.org/0000-0001-6210-7389","observed_orcids":["https://orcid.org/0000-0001-6210-7389"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hauer, Daniel","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":0,"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":0.7333999872207642,"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":0.7333999872207642,"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":0.18690000474452972,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.055799998342990875,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/fundamental-gap","display_name":"fundamental band gap","score":0.8309999704360962},{"id":"https://openalex.org/keywords/convex-potentials","display_name":"convex potential","score":0.9480000138282776},{"id":"https://openalex.org/keywords/convex-domains","display_name":"convex domains","score":0.8600000143051147},{"id":"https://openalex.org/keywords/first-eigenvalue","display_name":"first eigenvalue","score":0.7059999704360962},{"id":"https://openalex.org/keywords/weighted-poincare-inequality","display_name":"weighted Poincar\u00e9 inequality","score":0.8619999885559082},{"id":"https://openalex.org/keywords/quantitative-stability","display_name":"quantitative stability","score":0.4449999928474426},{"id":"https://openalex.org/keywords/degenerate-elliptic-operators","display_name":"degenerate elliptic operators","score":0.6809999942779541},{"id":"https://openalex.org/keywords/one-dimensional-domain","display_name":"one-dimensional domain","score":0.35499998927116394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8417999744415283},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6772000193595886},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5742999911308289},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5076000094413757},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.4950000047683716},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.43140000104904175},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.40230000019073486},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.3928000032901764},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3873000144958496},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.37880000472068787},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.36399999260902405},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.35429999232292175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3181000053882599},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C102231394","wikidata":"https://www.wikidata.org/wiki/Q5280763","display_name":"Dirichlet eigenvalue","level":5,"score":0.3082999885082245},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27219998836517334},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.26649999618530273},{"id":"https://openalex.org/C2991999034","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex domain","level":3,"score":0.26579999923706055},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2639000117778778}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.13443","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13443","pdf_url":"https://arxiv.org/pdf/2608.13443","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.2608.13443","doi":"https://doi.org/10.48550/arxiv.2608.13443","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.13443","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:2608.13443","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.13443","pdf_url":"https://arxiv.org/pdf/2608.13443","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203487615.pdf","grobid_xml":"https://content.openalex.org/works/W7203487615.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2127874460","https://openalex.org/W7094302782","https://openalex.org/W3163925918","https://openalex.org/W1517933918","https://openalex.org/W7223091403","https://openalex.org/W3028538784","https://openalex.org/W7127892460","https://openalex.org/W1883100128","https://openalex.org/W1999672863","https://openalex.org/W3004485912"],"abstract_inverted_index":{"We":[0,13,32,49],"study":[1],"the":[2,6,16,28,52,85,97,108,112,121,127],"fundamental":[3],"gap":[4,103],"of":[5,84,107],"Dirichlet":[7],"$p$-Laplacian":[8],"on":[9,67,78],"bounded":[10],"convex":[11,89],"domains.":[12],"first":[14,86,109],"prove":[15],"sharp":[17],"one-dimensional":[18],"estimate":[19],"$\u0393_p(I_D,V)\\ge":[20],"(p-1)(2^p-1)(\u03c0_p/D)^p$,":[21],"$I_D=(-D/2,D/2)$,":[22],"for":[23,43,96,126],"all":[24],"$12$,":[25],"$G_{p,N}>0$":[26],"and":[27,37,47,59,100,111,123],"infimum":[29],"is":[30,65],"attained.":[31],"obtain":[33],"explicit":[34],"dimension-dependent":[35],"bounds":[36],"$G_{p,N}\\asymp_p":[38],"N^{p-2}$":[39],"as":[40,54],"$N\\to\\infty$,":[41],"while":[42],"fixed":[44],"$N$,":[45],"$\\lim_{p\\downarrow2}G_{p,N}=3\u03c0^2$":[46],"$\\lim_{p\\to\\infty}G_{p,N}^{1/p}=4$.":[48],"also":[50,119],"characterize":[51],"collapse":[53],"$p\\downarrow2$:":[55],"minimizing":[56],"domains":[57],"degenerate,":[58],"every":[60],"limiting":[61],"normalized":[62],"ground-state":[63,98],"measure":[64],"supported":[66],"a":[68,91,101],"unit":[69],"segment":[70],"and,":[71],"up":[72],"to":[73],"rigid":[74],"motions,":[75],"equals":[76],"$2\\cos^2(\u03c0t)\\,dt$":[77],"$(-1/2,1/2)$.":[79],"The":[80],"proof":[81],"establishes":[82],"log-concavity":[83],"$p$-eigenfunction":[87],"with":[88],"potential,":[90],"degenerate":[92],"weighted":[93,114],"Poincar\u00e9":[94,115],"inequality":[95],"measure,":[99],"lower":[102],"bound":[104],"in":[105],"terms":[106],"eigenvalue":[110],"associated":[113],"constant.":[116],"These":[117],"estimates":[118],"give":[120],"compactness":[122],"equality":[124],"analysis":[125],"collapsing":[128],"minimizers.":[129]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-15T00:00:00"}
