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arXiv · 1510.02612

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

Dominic Breit·Andrea Cianchi·Lars Diening·Tuomo Kuusi·Sebastian Schwarzacher
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Abstract

Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calderón-Zygmund theory in terms of Calderón-Zygmund singular integrals, 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. In particular, new gradient estimates are exhibited, and well-known results in customary function spaces are easily recovered.

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Dominic Breit, Andrea Cianchi, Lars Diening, Tuomo Kuusi, Sebastian Schwarzacher. 2015-10-09. Pointwise Calderón-Zygmund gradient estimates for the $p$-Laplace system. https://arxiv.org/abs/1510.02612

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