This talk focusses on the smoothness of the solutions of parabolic PDEs on Lipschitz domains in the fractional Sobolev scale Hs, s in R. The regularity in these spaces is related with the approximation order that can be achieved by numerical schemes based on uniform grid refinements. The results presented provide a first attempt to generalize the well-known H3/2-Theorem of Jerison and Kenig to parabolic PDEs. As a special case the heat equation on radial-symmetric cones is investigated.
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