Potential estimates for the p-Laplace system with data in divergence form

Andrea Cianchi, Sebastian Schwarzacher

Published 2017-10-31Version 1

A pointwise bound for local weak solutions to the p-Laplace system is established in terms of data on the right-hand side in divergence form. The relevant bound involves a Havin-Maz'ya- Wulff potential of the datum, and is a counterpart for data in divergence form of a classical result of [KiMa], that has recently been extended to systems in [KuMi2]. A local bound for oscillations is also provided. These results allow for a unified approach to regularity estimates for broad classes of norms, including Banach function norms (e.g. Lebesgue, Lorentz and Orlicz norms), and norms depending on the oscillation of functions (e.g. Holder, BMO and, more generally, Campanato type norms). In particular, new regularity properties are exhibited, and well-known results are easily recovered.