{"paper":{"title":"Boundary singularities of solutions of semilinear elliptic equations with critical Hardy potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konstantinos T. Gkikas, Laurent Veron","submitted_at":"2014-10-05T17:04:46Z","abstract_excerpt":"We study the boundary behaviour of the of (E) $-\\Gd u-\\myfrac{\\xk }{d^2(x)}u+g(u)=0$, where $0<\\xk <\\frac{1}{4}$ and $g$ is a continuous nonndecreasing function in a bounded convex domain of $\\BBR^N$. We first construct the Martin kernel associated to the the linear operator $\\CL_{\\xk }=-\\Gd-\\frac{\\xk }{d^2(x)}$ and give a general condition for solving equation (E) with any Radon measure $\\gm$ for boundary data. When $g(u)=|u|^{q-1}u$ we show the existence of a critical exponent $q_c=q_c(N,\\xk )>1$: when $0<q<q_c$ any measure is eligible for solving (E) with $\\gm$ for boundary data; if $q\\geq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1176","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"}