{"paper":{"title":"Reduced limit for semilinear boundary value problems with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Mousomi Bhakta","submitted_at":"2012-10-11T14:30:30Z","abstract_excerpt":"We study boundary value problems for semilinear elliptic equations of the form $-\\Delta u+g\\circ u=\\mu$ in a smooth bounded domain $\\Omega\\subset R^N$. Let $\\{\\mu_n\\}$ and $\\{\\tau_n\\}$ be sequences of measure in $\\Omega$ and $\\partial \\Omega$ respectively. Assume that there exists a solution $u_n$ of the equation with $\\mu=\\mu_n$ subject to boundary data $\\tau_n$. Further assume that the sequences of measures converge in a weak sense to $\\mu$ and $\\tau$ respectively and $\\{u_n\\}$ converges to $u$ in $L^1(\\Omega)$. In general $u$ is not a solution of the boundary value problem with data $(\\mu,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3254","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"}