| | |
Summary: to appear in "Duke Mathematical Journal".
GRADIENT ESTIMATES
FOR A CLASS OF PARABOLIC SYSTEMS
EMILIO ACERBI AND GIUSEPPE MINGIONE
Abstract. We establish local CalderŽon & Zygmund type estimates for a class of par-
abolic problems whose model is the non-homogeneous, degenerate/singular parabolic
p-Laplacean system
ut - div(|Du|p-2
Du) = div(|F|p-2
F) ,
proving that
F Lq
loc = Du Lq
loc q p .
We also treat systems with discontinuous coefficients of VMO type.
1. Introduction
The aim of this paper is to present CalderŽon-Zygmund type estimates for weak solu-
tions to a class of degenerate/singular parabolic systems, and equations, a prominent
model example of which is the non-homogeneous, parabolic p-Laplacean system
ut - div(|Du|p-2
|
