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

By Dominic Breit, Andrea Cianchi, Lars Diening, Tuomo Kuusi, Sebastian Schwarzacher. Journal des Mathématiques Pures et Appliquées, 2015

55 citations recorded by the source corpus.

Abstract Pointwise estimates for the gradient of solutions to the p-Laplace system with right-hand 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 Calderon–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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f8de486c30d48f0034edecb85dd4a3af04a5416

Citations in the corpus

• Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems (2017, unknown): “This includes the classics [17,27,28,33,37,38,43,44,58,60–62], and the newer advances [11,13,13,14,22,31,41].”