{"paper":{"title":"On the $p$-Laplacian with Robin boundary conditions and boundary trace theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Hynek Kovarik, Konstantin Pankrashkin","submitted_at":"2016-03-05T15:42:33Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^\\nu$, $\\nu\\ge 2$, be a $C^{1,1}$ domain whose boundary $\\partial\\Omega$ is either compact or behaves suitably at infinity. For $p\\in(1,\\infty)$ and $\\alpha>0$, define \\[ \\Lambda(\\Omega,p,\\alpha):=\\inf_{\\substack{u\\in W^{1,p}(\\Omega)\\\\ u\\not\\equiv 0}}\\dfrac{\\displaystyle \\int_\\Omega |\\nabla u|^p \\mathrm{d} x - \\alpha\\displaystyle\\int_{\\partial\\Omega} |u|^p\\mathrm{d}\\sigma}{\\displaystyle\\int_\\Omega |u|^p\\mathrm{d} x}, \\] where $\\mathrm{d}\\sigma$ is the surface measure on $\\partial\\Omega$. We show the asymptotics \\[ \\Lambda(\\Omega,p,\\alpha)=-(p-1)\\alpha^{\\frac{p}{p-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01737","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"}