{"paper":{"title":"Overdetermined problems for the normalized $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Bernd Kawohl","submitted_at":"2017-11-23T14:01:17Z","abstract_excerpt":"We extend the symmetry result of Serrin and Weinberger from the Laplacian operator to the highly degenerate game-theoretic $p$-Laplacian operator and show that viscosity solutions of $-\\Delta_p^Nu=1$ in $\\Omega$, $u=0$ and $\\tfrac{\\partial u}{\\partial\\nu}=-c\\neq 0$ on $\\partial\\Omega$ can only exist on a bounded domain $\\Omega$ if $\\Omega$ is a ball."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08696","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"}