{"paper":{"title":"Optimal results for the fractional heat equation involving the Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Primo, Boumediene Abdellaoui, Ireneo Peral, Mar\\'ia Medina","submitted_at":"2014-12-28T12:43:46Z","abstract_excerpt":"In this paper we study the influence of the Hardy potential in the fractional heat equation. In particular, we consider the problem $$(P_\\theta)\\quad \\left\\{ \\begin{array}{rcl} u_t+(-\\Delta)^{s} u&=&\\l\\dfrac{\\,u}{|x|^{2s}}+\\theta u^p+ c f\\mbox{ in } \\Omega\\times (0,T),\\\\ u(x,t)&>&0\\inn \\Omega\\times (0,T),\\\\ u(x,t)&=&0\\inn (\\ren\\setminus\\Omega)\\times[ 0,T),\\\\ u(x,0)&=&u_0(x) \\mbox{ if }x\\in\\O, \\end{array} \\right. $$ where $N> 2s$, $0<s<1$, $(-\\Delta)^s$ is the fractional Laplacian of order $2s$, $p>1$, $c,\\l>0$, $u_0\\ge 0$, $f\\ge 0$ are in a suitable class of functions and $\\theta=\\{0,1\\}$. Not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8159","kind":"arxiv","version":3},"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"}