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Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm
We determine the exact regularity of the trace of a function $u \in L_{q} (0,T; W_{p}^{2}(\Omega ))$ $\cap W^{1}_{q} (0,T; {L_{p} (\Omega ))}$ and of the trace of its spatial gradient on $\partial \Omega \times ( 0,T )$ in the regime $p \le q$. While for $p=q$ both the spatial …