Besov regularity of parabolic and hyperbolic PDEs

This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in the specific scale $\ B^r_{\tau,\tau}, \ \frac{1}{\tau}=\frac{r}{d}+\frac{1}{p}\ $ of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms.