{"paper":{"title":"Some overdetermined problems related to the anisotropic capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chiara Bianchini, Giulio Ciraolo, Paolo Salani","submitted_at":"2018-03-13T16:13:36Z","abstract_excerpt":"We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler $p$-capacity of a convex set $\\Omega \\subset \\mathbb{R}^N$, with $1<p<N$. In particular we show that if the Finsler $p$-capacitary potential $u$ associated to $\\Omega$ has two homothetic level sets then $\\Omega$ is Wulff shape. Moreover, we show that the concavity exponent of $u$ is $q=-(p-1)/(N-p)$ if and only if $\\Omega$ is Wulff shape."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04911","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"}