Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields

In this paper we pose the $\infty$-Laplace Equation as a Dirichlet Problem in class of Grushin-type spaces whose vector fields are form \begin{equation*} X_k(p):=\sigma_k(p)\frac{\partial}{\partial x_k} \end{equation*} and $\sigma_k$ is not polynomial for indices $m+1 \leq k n$. Solutions to $\infty$-Laplacian viscosity sense have been shown exist be unique [3], when polynomial; extend these results by exploiting relationship between Euclidean second-order jets utilizing estimates on derivatives sub- supersolutions order produce comparison principle semicontinuous functions.