The infinity(x)-equation in Grushin-type spaces

Abstract

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

Keywords

• Viscosity solutions
• Grushin-type spaces
• Infinite Laplacian