{"paper":{"title":"Measure boundary value problem for 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 Gkikas (CMM), Laurent Veron (LMPT)","submitted_at":"2014-10-05T19:42:27Z","abstract_excerpt":"Let $\\Omega\\subset\\BBR^N$ be a bounded $C^2$ domain and $\\CL_\\gk=-\\Gd-\\frac{\\gk}{d^2}$ the Hardy operator where $d=\\dist (.,\\prt\\Gw)$ and $0<\\gk\\leq\\frac{1}{4}$. Let $\\ga_{\\pm}=1\\pm\\sqrt{1-4\\gk}$ be the two Hardy exponents, $\\gl_\\gk$ the first eigenvalue of $\\CL_\\gk$ with corresponding positive eigenfunction $\\phi_\\gk$. If $g$ is a continuous nondecreasing function satisfying $\\int_1^\\infty(g(s)+|g(-s)|)s^{-2\\frac{2N-2+\\ga_+}{2N-4+\\ga_+}}ds<\\infty$, then for any Radon measures $\\gn\\in \\GTM_{\\phi_\\gk}(\\Gw)$ and $\\gm\\in \\GTM(\\prt\\Gw)$ there exists a unique weak solution to problem $P_{\\gn,\\gm}$:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1201","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"}