{"paper":{"title":"An isoperimetric result for the fundamental frequency via domain derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carlo Nitsch","submitted_at":"2012-01-25T17:17:39Z","abstract_excerpt":"The Faber-Krahn deficit $\\delta\\lambda$ of an open bounded set $\\Omega$ is the normalized gap between the values that the first Dirichlet Laplacian eigenvalue achieves on $\\Omega$ and on the ball having same measure as $\\Omega$. For any given family of open bounded sets of $\\R^N$ ($N\\ge 2$) smoothly converging to a ball, it is well known that both $\\delta\\lambda$ and the isoperimetric deficit $\\delta P$ are vanishing quantities. It is known as well that, at least for convex sets, the ratio $\\frac{\\delta P}{\\delta \\lambda}$ is bounded by below by some positive constant (see \\cite{BNT,PW}), and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5328","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"}