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.