Green's function of non-linear degenerate elliptic operators and its application to regularity

Abstract

We are concerned with the Green's function associated with the non-linear degenerate elliptic operator of divergence form. We present several theorems on local estimates and comparisons with the p-Laplacian for the Green's function under certain conditions in the sense of distributions. As an application of these estimates of the Green's function, the regularity in Morrey spaces of the so-called inhomogeneous A-harmonic equation is derived.