Regularity estimates for nonlocal space-time master equations in bounded domains

Abstract

We obtain sharp parabolic interior and global Schauder estimates for solutions to nonlocal space-time master equations $({\partial }_t+L{)}^{s}u=f$ in $\mathbb{R}\times \Omega$, where $L$ is an elliptic operator in divergence form, subject to homogeneous Dirichlet and Neumann boundary conditions. In particular, we establish the precise behavior of solutions near the boundary. Along the way, we prove a characterization of the correct intermediate parabolic Hölder spaces in the spirit of Sergio Campanato.

49 pages. To appear in Journal of Evolution Equations