Existence results for nonlinear cone degenerate Laplace equations

Abstract

This paper concerns a class of non-divergence nonlinear elliptic equations driven by the cone degenerate Laplacian, which is motivated by cone calculus. We establish the existence of viscosity solutions by proving the Alexandrov-Bakelman-Pucci and Hölder estimates. Furthermore, we obtain the existence of weak solutions by proving the equivalence between weak solutions and viscosity solutions.