{"paper":{"title":"Regularity results for a class of mixed local and nonlocal singular problems involving distance function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kaushik Bal, Stuti Das","submitted_at":"2024-11-21T15:27:21Z","abstract_excerpt":"We investigate the following mixed local and nonlocal quasilinear equation with singularity given by \\begin{eqnarray*} \\begin{split} -\\Delta_pu+(-\\Delta)_q^s u&=\\frac{f(x)}{u^{\\delta}}\\text { in } \\Omega, \\\\u&>0 \\text{ in } \\Omega,\\\\u&=0 \\text { in }\\mathbb{R}^n \\backslash \\Omega; \\end{split} \\end{eqnarray*} where, \\begin{equation*} (-\\Delta )_q^s u(x):= c_{n,s}\\operatorname{P.V.}\\int_{\\mathbb{R}^n}\\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y))}{|x-y|^{n+sq}} d y, \\end{equation*} with $\\Omega$ being a bounded domain in $\\mathbb{R}^{n}$ with $C^2$ boundary, $1<q\\leq p<\\infty$, $s\\in(0,1)$, $\\delta>0$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14217","kind":"arxiv","version":2},"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/2411.14217/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"}