{"paper":{"title":"p(x)-Harmonic functions with unbounded exponent in a subdomain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e Miguel Urbano, Juan J. Manfredi, Julio D. Rossi","submitted_at":"2008-09-16T15:14:24Z","abstract_excerpt":"We study the Dirichlet problem $-\\div(|\\nabla u|^{p(x)-2} \\nabla u) =0 $ in $\\Omega$, with $u=f$ on $\\partial \\Omega$ and $p(x) = \\infty$ in $D$, a subdomain of the reference domain $\\Omega$. The main issue is to give a proper sense to what a solution is. To this end, we consider the limit as $n \\to \\infty$ of the solutions $u_n$ to the corresponding problem when $p_n(x) =p(x) \\wedge n$, in particular, with $p_n = n$ in $D$. Under suitable assumptions on the data, we find that such a limit exists and that it can be characterized as the unique solution of a variational minimization problem whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.2731","kind":"arxiv","version":4},"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"}