{"paper":{"title":"On an eigenvalue problem associated with mixed operators under mixed boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Lovelesh Sharma, Tuhina Mukherjee","submitted_at":"2024-11-25T15:37:08Z","abstract_excerpt":"In this paper, we study a class of eigenvalue problems involving both local as well as nonlocal operators, precisely the classical Laplace operator and the fractional Laplace operator in the presence of mixed boundary conditions, that is\n  \\begin{equation} \\label{1}\n  \\left\\{\\begin{split} \\mathcal{L}u\\: &= \\lambda u,~~u>0~ \\text{in} ~\\Omega,\n  u&=0~~\\text{in} ~~{U^c},\n  \\mathcal{N}_s(u)&=0 ~~\\text{in} ~~{\\mathcal{N}},\n  \\frac{\\partial u}{\\partial \\nu}&=0 ~~\\text{in}~~ \\partial \\Omega \\cap \\overline{\\mathcal{N}},\n  \\end{split} \\right.\\tag{$P_\\lambda$} \\end{equation}\n  where $U= (\\Omega \\cup {\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16499","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16499/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}