{"paper":{"title":"Boundary Singularities on a Wedge-like Domain of a Semilinear Elliptic Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konstantinos T. Gkikas","submitted_at":"2017-03-26T09:22:38Z","abstract_excerpt":"Let $n\\geq2$ and $ \\Omega\\subset \\mathbb{R}^{n+1}$ be a Lipschitz wedge- like domain . We construct positive weak solutions of the problem $$\\Delta u + u^p = 0 \\quad\\hbox{in}\\, \\Omega,$$ which vanish in a suitable trace sense on $\\partial\\Omega,$ but which are singular at prescribed \"edge\" of $\\Omega$ if $p$ is equal or slightly above a certain exponent $p_0>1$ which depends on $\\Omega.$ Moreover, in the case which $\\Omega$ is unbounded, the solutions have fast decay at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08793","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"}