Improved Holder regularity for strongly elliptic PDEs

We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of Holder regularity, higher than what is given by the classical exponent 1/K. (C) 2020 Elsevier Masson SAS. All rights reserved.