{"paper":{"title":"Classical solutions and higher regularity for nonlinear fractional diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Rodr\\'iguez, Arturo de Pablo, Fernando Quir\\'os, Juan Luis V\\'azquez","submitted_at":"2013-11-28T21:12:09Z","abstract_excerpt":"We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$ \\partial_tu+(-\\Delta)^{\\sigma/2}\\varphi(u)=0, $$ posed for $x\\in \\mathbb{R}^N$, $t>0$, with $0<\\sigma<2$, $N\\ge1$. If the nonlinearity satisfies some not very restrictive conditions: $\\varphi\\in C^{1,\\gamma}(\\mathbb{R})$, $1+\\gamma>\\sigma$, and $\\varphi'(u)>0$ for every $u\\in\\mathbb{R}$, we prove that bounded weak solutions are classical solutions for all positive times. We also explore sufficient conditions on the non-linearity to obtain higher regularity for the solutions, even $C^\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7427","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"}