{"paper":{"title":"An elliptic semilinear equation with source term and boundary measure data: the supercritical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giang Hoang (LMPT), Laurent V\\'eron (LMPT), Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Quoc-Hung Nguyen (LMPT)","submitted_at":"2014-12-16T15:29:46Z","abstract_excerpt":"We give new criteria for the existence of weak solutions to an equation with a super linear source term \\begin{align*}-\\Delta u = u^q ~~\\text{in}~\\Omega,~~u=\\sigma~~\\text{on }~\\partial\\Omega\\end{align*}where $\\Omega$ is a either a bounded smooth domain or $\\mathbb{R}\\_+^{N}$, $q\\textgreater{}1$  and $\\sigma\\in \\mathfrak{M}^+(\\partial\\Omega)$ is a nonnegative Radon measure on $\\partial\\Omega$.  One of the criteria we obtain is expressed in terms of some Bessel capacities on $\\partial\\Omega$. We also give a sufficient condition for the existence of weak solutions to equation with source mixed te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5044","kind":"arxiv","version":5},"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"}