Parabolic Initial-Boundary Value Problems with Inhomogeneous Data A Maximal Weighted Regularity Approach

by N. Lindemulder

Institution: Universiteit Utrecht
Year: 2015
Keywords: parabolic initial-boundary value problems, inhomogeneous data, maximal regularity, Muckenhaupt (power) weights, traces, anisotropic mixed-norm function spaces, maximal functions, UMD spaces, Fourier multipliers
Record ID: 1264275
Full text PDF: http://dspace.library.uu.nl:8080/handle/1874/307054


We develop a new function space theoretic weighted $L^{q}$-$L^{p}$-maximal regularity approach for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, and yield flexibility in the optimal regularity of the initial-boundary data. The novelty of our approach is the use of weighted anisotropic mixed-norm Banach space-valued function spaces of Sobolev, Bessel potential, Triebel-Lizorkin, and Besov type. The main tools are maximal functions and Fourier multipliers, of which we also give a detailed treatment.