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

Abstract

We determine the exact regularity of the trace of a function (Formula Presented) 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 6 ≠ q the Lizorkin-Triebel spaces turn out to be necessary for characterizing the sharp temporal regularity. © 2002 American Mathematical Society.