Fundamental solutions to the p-Laplace equation in a class of Grushin vector fields

Abstract

We find the fundamental solution to the p-Laplace equation in a class of Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in Euclidean space. We then use this solution to find an infinite harmonic function with specific boundary data and to compute the capacity of annuli centered at the singularity.

Keywords

• Grushin-type spaces
• p-Laplacian