{"paper":{"title":"On the boundary of the attainable set of the Dirichlet spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aldo Pratelli, Carlo Nitsch, Lorenzo Brasco","submitted_at":"2011-12-20T13:56:48Z","abstract_excerpt":"Denoting by $\\mathcal{E}\\subseteq \\R^2$ the set of the pairs $(\\lambda_1(\\Omega),\\lambda_2(\\Omega))$ for all the open sets $\\Omega\\subseteq\\R^N$ with unit measure, and by $\\Theta\\subseteq\\R^N$ the union of two disjoint balls of half measure, we give an elementary proof of the fact that $\\partial\\E$ has horizontal tangent at its lowest point $(\\lambda_1(\\Theta),\\lambda_2(\\Theta))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4689","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"}