{"paper":{"title":"On the torsion function with Robin or Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"D. Bucur, M. van den Berg","submitted_at":"2013-05-09T16:25:19Z","abstract_excerpt":"For $p\\in (1,+\\infty)$ and $b \\in (0, +\\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\\Om \\subset \\R^m$ satisfies formally the equation $-\\Delta_p =1$ in $\\Om$ and $|\\nabla u|^{p-2} \\frac{\\partial u}{\\partial n} + b|u|^{p-2} u =0$ on $\\partial \\Om$. We obtain bounds of the $L^\\infty$ norm of $u$ {\\it only} in terms of the bottom of the spectrum (of the Robin $p$-Laplacian), $b$ and the dimension of the space in the following two extremal cases: the linear framework (corresponding to $p=2$) and arbitrary $b>0$, and the non-linear framework "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2137","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"}