Electronic Journal of Differential Equations (Jun 2011)

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

  • Thomas Bieske

Journal volume & issue
Vol. 2011, no. 84,
pp. 1 – 10

Abstract

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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.

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