{"paper":{"title":"Moderate solutions of semilinear elliptic equations with Hardy potential under minimal restrictions on the potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Vitaly Moroz","submitted_at":"2016-03-30T16:20:44Z","abstract_excerpt":"We study semilinear elliptic equations with Hardy potential $\\mathrm{(E)} \\; -L_\\mu u+u^q=0$ in a bounded smooth domain $\\Omega\\subset \\mathbb R^N$. Here $q>1$, $L_\\mu=\\Delta+\\frac{\\mu}{\\delta_\\Omega^2}$ and $\\delta_\\Omega(x)=\\mathrm{dist}(x,\\partial\\Omega)$. Assuming that $0\\leq \\mu<C_H(\\Omega)$, boundary value problems with measure data and discrete boundary singularities for positive solutions of $\\mathrm{(E)}$ have been studied earlier. In the present paper we study these problems, in arbitrary domains, assuming only $-\\infty<\\mu<1/4$, even if $C_H(\\Omega)<1/4$. We recall that $C_H(\\Omega)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09265","kind":"arxiv","version":3},"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"}