Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 84, pp. 110.
Fundamental solutions to the pLaplace equation in a class
of Grushin vector fields
Thomas Bieske
Abstract:
We find the fundamental solution to the pLaplace equation
in a class of Grushintype spaces. The singularity occurs
at the subRiemannian 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: Grushintype spaces; pLaplacian.
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Thomas Bieske
Department of Mathematics
University of South Florida
Tampa, FL 33620, USA
email: tbieske@math.usf.edu

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