{"paper":{"title":"On fractional p-laplacian parabolic problem with general data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmed Attar, Boumediene Abdellaoui, Ireneo Peral, Rachid Bentifour","submitted_at":"2016-12-05T10:50:59Z","abstract_excerpt":"In this article the problem to be studied is the following $$ (P) \\left\\{ \\begin{array}{rcll} u_t+(-\\D^s_{p}) u & = & f(x,t) & \\text{ in } \\O_{T}\\equiv \\Omega \\times (0,T), \\\\ u & = & 0 & \\text{ in }(\\ren\\setminus\\O) \\times (0,T), \\\\ u & \\ge & 0 & \\text{ in }\\ren \\times (0,T),\\\\ u(x,0) & = & u_0(x) & \\mbox{ in }\\O, \\end{array}% \\right. $$ where $\\Omega$ is a bounded domain, and $(-\\D^s_{p})$ is the fractional p-Laplacian operator defined by $$ (-\\D^s_{p})\\, u(x,t):=P.V\\int_{\\ren} \\,\\dfrac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}} \\,dy$$ with $1<p<N$, $s\\in (0,1)$ and $f, u_0$ are mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01301","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"}