{"paper":{"title":"Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Matteo Bonforte, Xavier Ros-Oton","submitted_at":"2015-10-13T16:09:18Z","abstract_excerpt":"We study the positivity and regularity of solutions to the fractional porous medium equations $u_t+(-\\Delta)^su^m=0$ in $(0,\\infty)\\times\\Omega$, for $m>1$ and $s\\in (0,1)$ and with Dirichlet boundary data $u=0$ in $(0,\\infty)\\times({\\mathbb R}^N\\setminus\\Omega)$, and nonnegative initial condition $u(0,\\cdot)=u_0\\geq0$.\n  Our first result is a quantitative lower bound for solutions which holds for all positive times $t>0$. As a consequence, we find a global Harnack principle stating that for any $t>0$ solutions are comparable to $d^{s/m}$, where $d$ is the distance to $\\partial\\Omega$. This is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03758","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"}