{"paper":{"title":"Semilinear elliptic inequalities in the exterior of a compact set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marius Ghergu, Steven D. Taliaferro","submitted_at":"2010-11-21T19:10:21Z","abstract_excerpt":"We study the semilinear elliptic inequality $-\\Delta u\\geq\\varphi(\\delta_K(x))f(u)$ in $R^N\\setminus K,$ where $\\varphi, f$ are non-negative and continuous functions, $K\\subset R^N$ $(N\\geq 2)$ is a compact set and $\\delta_K(x)={\\rm dist}(x,\\partial K)$. We obtain optimal conditions in terms of $\\varphi$ and $f$ for the existence of $C^2$ positive solutions. Our analysis emphasizes the role played by the geometry of the compact set $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4691","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"}