The infinity(x)-Laplace equation in Riemannian vector fields

Abstract

We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of viscosity solutions to the infinity(x)-Laplace equation in Riemannian vector fields. Due to the differences between Euclidean jets and Riemannian jets, the Euclidean method of proof is not valid in this environment.

Keywords

• Viscosity solution
• Riemannian vector field
• infinite Laplacian