{"paper":{"title":"Boundary regularity for the fractional heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xavier Fern\\'andez-Real, Xavier Ros-Oton","submitted_at":"2014-11-30T20:12:21Z","abstract_excerpt":"We study the regularity up to the boundary of solutions to fractional heat equation in bounded $C^{1,1}$ domains.\n  More precisely, we consider solutions to $\\partial_t u + (-\\Delta)^s u=0 \\textrm{ in }\\Omega,\\ t > 0$, with zero Dirichlet conditions in $\\mathbb{R}^n\\setminus \\Omega$ and with initial data $u_0\\in L^2(\\Omega)$. Using the results of the second author and Serra for the elliptic problem, we show that for all $t>0$ we have $u(\\cdot, t)\\in C^s(\\mathbb{R}^n)$ and $u(\\cdot, t)/\\delta^s \\in C^{s-\\epsilon}(\\overline\\Omega)$ for any $\\epsilon > 0$ and $\\delta(x) = \\textrm{dist}(x,\\partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0275","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"}