The $\mathrm{\infty }(x)$-equation in Grushin-type Spaces

We employ Grushin jets which are adapted to the geometry of Grushin-type spaces to obtain the existence-uniqueness of viscosity solutions to the $\mathrm{\infty }(x)$-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.