Pointwise Calderón-Zygmund gradient estimates for the p-Laplace system

Dominic Breit, Andrea Cianchi, Lars Diening, Tuomo Kuusi, Sebastian Schwarzacher

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13 Citations (Scopus)
24 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)146-190
Number of pages45
JournalJournal de Mathématiques Pures et Appliquées
Volume114
Early online date1 Aug 2017
DOIs
Publication statusE-pub ahead of print - 1 Aug 2017

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