{"paper":{"title":"An existence result for a nonlinear transmission problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"G. Mishuris, M. Dalla Riva","submitted_at":"2014-08-22T13:04:33Z","abstract_excerpt":"Let $\\Omega^o$ and $\\Omega^i$ be open bounded subsets of $\\mathbb{R}^n$ of class $C^{1,\\alpha}$ such that the closure of $\\Omega^i$ is contained in $\\Omega^o$. Let $f^o$ be a function in $C^{1,\\alpha}(\\partial\\Omega^o)$ and let $F$ and $G$ be continuous functions from $\\partial\\Omega^i\\times\\mathbb{R}$ to $\\mathbb{R}$. By exploiting an argument based on potential theory and on the Leray-Schauder principle we show that under suitable and completely explicit conditions on $F$ and $G$ there exists at least one pair of continuous functions $(u^o, u^i)$ such that \\[ \\left\\{ \\begin{array}{ll} \\Delta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5287","kind":"arxiv","version":2},"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"}