Viscosity solutions to the ∞-Laplace equation in Grushin-type spaces

Abstract

In this paper, we prove the existence and uniqueness of viscosity solutions to the infinite Laplace equation in Grushin-type spaces whose tangent spaces consist of arbitrary triangular vector fields.

Keywords

• p-laplace equation
• ∞-laplace equation
• viscosity solution
• grushin-type spaces
• sub-riemannian geometry