{"paper":{"title":"Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Huyuan Chen","submitted_at":"2015-09-19T01:05:34Z","abstract_excerpt":"In this paper, we classify the singularities of nonnegative solutions to fractional elliptic equation \\begin{equation}\\label{eq 0.1}\n  \\arraycolsep=1pt \\begin{array}{lll}\n  \\displaystyle (-\\Delta)^\\alpha u=u^p\\quad\n  &{\\rm in}\\quad \\Omega\\setminus\\{0\\},\\\\[2mm]\n  \\phantom{ (-\\Delta)^\\alpha }\n  \\displaystyle u=0\\quad\n  &{\\rm in}\\quad \\mathbb{R}^N\\setminus\\Omega, \\end{array} \\end{equation} where $p>1$, $\\Omega$ is a bounded, $C^2$ domain in $\\mathbb{R}^N$ containing the origin, $N\\ge2$ and the fractional Laplacian $(-\\Delta)^\\alpha$ is defined in the principle value sense. We obtain that any clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05836","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":""},"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"}