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 is an element of L-q (0, T; W-p(2)(Omega)) boolean AND W-q(1) (0, T; L-p (Omega)) and of the trace of its spatial gradient on partial derivativeOmega x (0, T) in the regime p less than or equal to q. While for p = q both the spatial and temporal regularity of the traces can be completely characterized by fractional order Sobolev-Slobodetskii spaces, for p not equal q the Lizorkin-Triebel spaces turn out to be necessary for characterizing the sharp temporal regularity.