{"paper":{"title":"Minimization and Steiner symmetry of the first eigenvalue for a fractional eigenvalue problem with indefinite weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Anedda, Fabrizio Cuccu, Silvia Frassu","submitted_at":"2019-04-05T08:08:29Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^N$, $N\\geq 2$, be an open bounded connected set. We consider the fractional weighted eigenvalue problem\n  $(-\\Delta)^s u =\\lambda \\rho u$ in $\\Omega$ with homogeneous Dirichlet boundary condition,\n  where $(-\\Delta)^s$, $s\\in (0,1)$, is the fractional Laplacian operator, $\\lambda \\in \\mathbb{R}$ and $ \\rho\\in L^\\infty(\\Omega)$. We study weak* continuity, convexity and G\\^ateaux differentiability of the map $\\rho\\mapsto1/\\lambda_1(\\rho)$, where $\\lambda_1(\\rho)$ is the first positive eigenvalue. Moreover, denoting by $\\mathcal{G}(\\rho_0)$ the class of rearrangements"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02923","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"}