Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed Lₚ-norm

We determine the exact regularity of the trace of a function u ∈ Lq (0,T; Wₚ²(Ω )) ∩ W¹q (0,T; Lₚ (Ω )) and of the trace of its spatial gradient on ∂ Ω × ( 0,T ) in the regime p ≤ 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 ≠ q the Lizorkin-Triebel spaces turn out to be necessary for characterizing the sharp temporal regularity.