{"paper":{"title":"The Effect of the Schwarz Rearrangement on the Periodic Principal Eigenvalue of a Nonsymmetric Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin (LJLL)","submitted_at":"2016-09-06T08:59:59Z","abstract_excerpt":"This paper is concerned with the periodic principal eigenvalue $k_\\lambda(\\mu)$ associated with the operator $- {d^2\\over dx^2} - 2\\lambda {d\\over dx} - \\mu(x) - \\lambda^2$ , (1) where $\\lambda\\in \\mathbb{R}$ and $\\mu$ is continuous and periodic in $x\\in\\mathbb{R}$. Our main result is that $k_\\lambda(\\mu^*) \\le k_\\lambda(\\mu)$, where $\\mu^*$ is the Schwarz rearrangement of the function $\\mu$. From a population dynamics point of view, using reaction-diffusion modeling, this result means that the fragmentation of the habitat of an invading population slows down the invasion. We prove that this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01442","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"}