{"paper":{"title":"Supercritical problems in domains with thin toroidal holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Seunghyeok Kim","submitted_at":"2013-06-01T12:26:17Z","abstract_excerpt":"In this paper we study the Lane-Emden-Fowler equation $$(P)_\\epsilon\\ \\{\\Delta u+|u|^{q-2}u=0 \\ \\hbox{in}\\ \\mathcal D_\\epsilon, u=0 \\ \\hbox{on}\\ \\partial\\mathcal D_\\epsilon.$$ Here $\\mathcal D_\\epsilon = \\mathcal D \\setminus \\{x \\in \\mathcal D \\ : \\ \\mathrm{dist}(x,\\Gamma_\\ell)\\le \\epsilon\\}$, $\\mathcal D$ is a smooth bounded domain in $\\mathbb{R}^N$, $\\Gamma_\\ell$ is an $\\ell-$dimensional closed manifold such that $\\Gamma_\\ell \\subset \\mathcal D$ with $1\\le \\ell \\le N-3$ and $q={2(N-\\ell)\\over N-\\ell-2}$. We prove that, under some symmetry assumptions, the number of sign changing solutions to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0099","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":""},"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"}