Higher order Calderon-Zygmund estimates for the p-Laplace equation

The paper is concerned with higher order Calderon-Zygmund estimates for the p-Laplace equation -div(A(del(u))) := - div (vertical bar del(u)vertical bar(p-2)del u) = -div F. 1 < p < infinity We are able to transfer local interior Besov and Triebel-Lizorkin regularity up to first order derivatives from the force term F to the flux A(del u). For p >= 2 we show that F is an element of B-Q,q(s) implies A(del u) is an element of B-Q,q(s) for any s is an element of (0, 1) and all reasonable Q, q is an element of (0, infinity] in the planar case. The result fails for p < 2. In case of higher dimensions and systems we have a smallness restriction on s. The quasi-Banach case 0 < min{Q, q} < 1 is included, since it has important applications in the adaptive finite element analysis. As an intermediate step we prove new linear decay estimates for p-harmonic functions in the plane for the full range 1 < p < infinity. (C) 2019 Elsevier Inc. All rights reserved.