{"paper":{"title":"A Neumann problem involving the $p(x)$-Laplacian with $p=\\infty$ in a subdomain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Yannakakis, Yiannis Karagiorgos","submitted_at":"2013-10-18T22:04:37Z","abstract_excerpt":"In this paper we study a non-homogeneous Neumann problem, where the $p(x)$-Laplacian is involved and $p=\\infty$ in a subdomain. By considering a suitable sequence $p_k$ of bounded variable exponents such that $p_k \\to p$ and replacing $p$ with $p_k$ in the original problem, we prove the existence of a solution $u_k$ for each of those intermediate ones. We show that the limit of the $u_k$ exists and after giving a variational characterization of it, in the part of the domain where $p$ is bounded, we show that it is a viscosity solution in the part where $p=\\infty$. Finally, we formulate the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5173","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"}