{"paper":{"title":"Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Luis Caffarelli, Tianling Jin, Yannick Sire","submitted_at":"2013-09-09T00:55:43Z","abstract_excerpt":"In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations $(-\\Delta)^\\sigma u=u^{\\frac{n+2\\sigma}{n-2\\sigma}}$ with an isolated singularity, where $\\sigma\\in (0,1)$. We prove that all the solutions are asymptotically radially symmetric. When $\\sigma =1$, these have been proved in \\cite{CGS} by Caffarelli, Gidas and Spruck."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2021","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"}