{"paper":{"title":"On Isolated Singularities of Fractional Semi-Linear Elliptic Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Yang, Wenming Zou","submitted_at":"2018-04-03T04:07:31Z","abstract_excerpt":"In this paper, we study the local behavior of nonnegative solutions of fractional semi-linear equations $(-\\Delta)^\\sigma u = u^p$ with an isolated singularity, where $\\sg \\in (0, 1)$ and $\\frac{n}{n-2\\sg} < p < \\frac{n+2\\sg}{n-2\\sg}$. We first use blow up method and a Liouville type theorem to derive an upper bound. Then we establish a monotonicity formula and a sufficient condition for removable singularity to give a classification of the isolated singularities. When $\\sg=1$, this classification result has been proved by Gidas and Spruck (Comm. Pure Appl. Math. 34: 525-598, 1981)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00817","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"}