{"paper":{"title":"Moderate solutions of semilinear elliptic equations with Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Phuoc-Tai Nguyen","submitted_at":"2014-07-14T09:08:34Z","abstract_excerpt":"Let $\\Omega$ be a bounded smooth domain in $\\mathbb{R}^N$. We study positive solutions of equation (E) $-L_\\mu u+ u^q = 0$ in $\\Omega$ where $L_\\mu=\\Delta + \\frac{\\mu}{\\delta^2}$,\n  $0<\\mu$, $q>1$ and $\\delta(x)=\\mathrm{dist}\\,(x,\\partial\\Omega)$. A positive solution of (E) is moderate if it is dominated by an $L_\\mu$-harmonic function. If $\\mu<C_H(\\Omega)$ (the Hardy constant for $\\Omega$) every positive $L_\\mu$- harmonic functions can be represented in terms of a finite measure on $\\partial\\Omega$ via the Martin representation theorem. However the classical measure boundary trace of any such"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3572","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"}