Maximal $$L^1$$-regularity for parabolic initial-boundary value problems with inhomogeneous data

MAXIMAL REGULARITY FOR ABSTRACT PARABOLIC PROBLEMS WITH INHOMOGENEOUS BOUNDARY DATA IN Lp-SPACES

Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal Lp-regularity is shown. By means of this purely operator theoretic approach, classical results on Lp-regularity of the diffusion equation with inhomogeneous Dirichle...

Maximal regularity and quasilinear parabolic boundary value problems

∂tw +A(v)w = f(v) in J̊ , w(0) = 0 has a unique solution w = w(v) ∈W(J). Clearly, a fixed point of the map v 7→ w(v) is a solution of (1). Fixed point arguments of this type are, of course, omnipresent in the study of evolution equations of type (1). The new feature of our work, which distinguishes it from all previous investigations, is that we assume that W(J) is a maximal regularity space and...

Initial - Boundary Value Problems for Parabolic Equations

Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data

In this paper we investigate vector-valued parabolic initial boundary value problems (A(t, x,D),Bj(t, x,D)) subject to general boundary conditions in domains G in R with compact C-boundary. The top-order coefficients of A are assumed to be continuous. We characterize optimal L-L-regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity conditio...

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...