Boundary regularity for the fractional heat equation

We study the regularity up to the boundary of solutions to fractional heat equation in bounded domains. More precisely, we consider solutions to , with zero Dirichlet conditions in and with initial data . Using the results of the second author and Serra for the elliptic problem, we show that for all we have and for any and . Our regularity results apply not only to the fractional Laplacian but also to more general integro-differential operators, namely those corresponding to stable L,vy processes. As a consequence of our results, we show that solutions to the fractional heat equation satisfy a Pohozaev-type identity for positive times.