Harnack inequality for degenerate and singular operators of p-Laplacian type on Riemannian manifolds

摘要

We study viscosity solutions to degenerate and singular elliptic equations of p-Laplacian type on Riemannian manifolds. The Krylov-Safonov type Harnack inequality for the p-Laplacian operators with is established on the manifolds with Ricci curvature bounded from below based on ABP type estimates. We also prove the Harnack inequality for nonlinear p-Laplacian type operators assuming that a nonlinear perturbation of Ricci curvature is bounded below.