ABP estimate and Harnack inequality for a class of degenerate fully nonlinear pseudo-$p$-Laplacian equations

Abstract

We prove Aleksandrov-Bakelman-Pucci estimates and Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear pseudo-$p$-Laplacian equations in nondivergence form. Our main approach is an adaptation of the sliding paraboloid method with anisotropic functions tailored to the coordinatewise degeneracy.

15 pages. A proof of ABP estimate is added