{"paper":{"title":"Strong competition versus fractional diffusion: the case of Lotka-Volterra interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Zilio, Gianmaria Verzini","submitted_at":"2013-10-28T09:42:02Z","abstract_excerpt":"We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem $$(-\\Delta)^s u_i = f_i(x,u_i) - \\beta u_i^p \\sum_{j\\neq i} a_{ij} u_j^p,$$ where $i = i,\\dots, k$, $s\\in(0,1)$, $p>0$, $a_{ij}>0$ and $\\beta>0$. When $k=2$ we develop a quasi-optimal regularity theory in $C^{0,\\alpha}$, uniformly w.r.t. $\\beta$, for every $\\alpha < \\alpha_{\\mathrm opt}=min(1,2s)$; moreover we show that the traces of the limiting profiles as $\\beta\\to+\\infty$ are Lipschitz continuous and segregated. Such results are extended to the case of $k\\geq3$ densi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7355","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"}