{"paper":{"title":"Self-generated interior blow-up solutions in fractional elliptic equation with absorption","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Huyuan Chen, Patricio Felmer","submitted_at":"2013-11-26T10:02:22Z","abstract_excerpt":"In this paper we study positive solutions to problem involving the fractional Laplacian $(E)$ $(-\\Delta)^{\\alpha} u(x)+|u|^{p-1}u(x)=0 in x\\in\\Omega\\setminus\\mathcal{C}$, subject to the conditions $u(x)=0$ $x\\in\\Omega^c$ and $\\lim_{x\\in\\Omega\\setminus\\mathcal{C}, x\\to\\mathcal{C}}u(x)=+\\infty$, where $p>1$ and $\\Omega$ is an open bounded $C^2$ domain in $\\mathbb{R}^N$, $\\mathcal{C}\\subset \\Omega$ is a compact $C^2$ manifold with $N-1$ multiples dimensions and without boundary, the operator $(-\\Delta)^{\\alpha}$ with $\\alpha\\in(0,1)$ is the fractional Laplacian.\n  We consider the existence of pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6607","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"}