The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates

Abstract

In this note we collect some very recent pointwise bounds for the gradient of solutions, and for the solutions themselves, to the p-Laplace system with right-hand side in divergence form. Both estimates inside the domain for local solutions, and global estimates for solutions to boundary value problems are discussed. Their formulation involves sharp maximal operators, whose properties enable us to translate some aspects of the elliptic regularity theory into a merely harmonic analytic framework. As a consequence, a flexible, comprehensive approach to estimates for solutions to the p-Laplace system for a broad class of norms is derived. In particular, global estimates under minimal boundary regularity are presented.