{"paper":{"title":"Non-energy semi-stable radial solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Salvador Villegas","submitted_at":"2014-05-06T12:17:12Z","abstract_excerpt":"This paper is devoted to the study of semi-stable radial solutions $u\\notin H^1(B_1)$ of $-\\Delta u=f(u) \\mbox{in} \\overline{B_1}\\setminus \\{0\\}=\\{x\\in \\mathbb{R}^N : 0<\\vert x\\vert\\leq 1\\}$, where $f\\in C^1(\\mathbb{R})$ and $N\\geq 2$. We establish sharp pointwise estimates for such solutions. In addition, we prove that in dimension $N=2$, any semi-stable radial weak solution of $-\\Delta u=f(u)$, posed in $B_1$ with Dirichlet data $u|_{\\partial B_1}=0$, is regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1241","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"}