{"paper":{"title":"On the $L^p$ norm of the torsion unction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michiel van den Berg, Thomas Kappeler","submitted_at":"2018-02-15T12:07:42Z","abstract_excerpt":"Bounds are obtained for the $L^p$ norm of the torsion function $v_{\\Omega}$, i.e. the solution of $-\\Delta v=1,\\, v\\in H_0^1(\\Omega),$ in terms of the Lebesgue measure of $\\Omega$ and the principal eigenvalue $\\lambda_1(\\Omega)$ of the Dirichlet Laplacian acting in $L^2(\\Omega)$. We show that these bounds are sharp for $1\\le p\\le 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05499","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"}