U. Biccari, M. Warma, E. Zuazua Local regularity for fractional heat equations<, Recent Advances in PDEs: Analysis, Numerics and Control, SEMA SIMAI Springer Series, Vol. 17 (2018). DOI: 10.1007/978-3-319-97613-6
Abstract: We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set \Omega\subset\mathbb{R}^N Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.
