TY - JOUR
T1 - Pointwise Calderón-Zygmund gradient estimates for the p-Laplace system
AU - Breit, Dominic
AU - Cianchi, Andrea
AU - Diening, Lars
AU - Kuusi, Tuomo
AU - Schwarzacher, Sebastian
PY - 2018/6
Y1 - 2018/6
N2 - Pointwise estimates for the gradient of solutions to the p-Laplace system with righthand side in divergence form are established. Their formulation involves the sharp maximal operator, whose properties enable us to develop a nonlinear counterpart of the classical Calderón–Zygmund theory for the Laplacian. As a consequence, a flexible, comprehensive approach to gradient bounds for the p-Laplace system for a broad class of norms is derived. The relevant gradient bounds are just reduced to norm inequalities for a classical operator of harmonic analysis. In particular, new gradient estimates are exhibited which augment the available literature in the elliptic regularity theory.
AB - Pointwise estimates for the gradient of solutions to the p-Laplace system with righthand side in divergence form are established. Their formulation involves the sharp maximal operator, whose properties enable us to develop a nonlinear counterpart of the classical Calderón–Zygmund theory for the Laplacian. As a consequence, a flexible, comprehensive approach to gradient bounds for the p-Laplace system for a broad class of norms is derived. The relevant gradient bounds are just reduced to norm inequalities for a classical operator of harmonic analysis. In particular, new gradient estimates are exhibited which augment the available literature in the elliptic regularity theory.
UR - https://www.scopus.com/pages/publications/85028335939
U2 - 10.1016/j.matpur.2017.07.011
DO - 10.1016/j.matpur.2017.07.011
M3 - Article
SN - 0021-7824
VL - 114
SP - 146
EP - 190
JO - Journal de Mathématiques Pures et Appliquées
JF - Journal de Mathématiques Pures et Appliquées
ER -