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In this paper we prove higher regularity for 2m-th order parabolic equationswith general boundary conditions. This is a kind of maximal L_p-L_q regularitywith differentiability, i.e. the main theorem is isomorphism between thesolution space and the data space using Besov and Triebel--Lizorkin spaces. Thekey is compatibility conditions for the initial data. We are able to get aunique smooth solution if the data satisfying compatibility conditions aresmooth.

Higher regularity for parabolic equations based on maximal L_p-L_q spaces