Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 84, pp. 1-10.

Title: Fundamental solutions to the p-Laplace equation in a class
       of Grushin vector fields
       
Author: Thomas Bieske (Univ. of South Florida, Tampa, FL, USA)
 
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.	 
	 
Submitted December 10, 2010. Published June 29, 2011.
Math Subject Classifications: 35H20, 53C17, 17B70
Key Words: Grushin-type spaces; p-Laplacian.