The 𝑃-Laplace equation on a class of Grushin-type spaces

Bieske, Thomas; Gong, Jasun

doi:10.1090/S0002-9939-06-08394-8

The $P$-Laplace equation on a class of Grushin-type spaces
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by Thomas Bieske and Jasun Gong PDF

Proc. Amer. Math. Soc. 134 (2006), 3585-3594 Request permission

Abstract:

We find the fundamental solution to the $P$-Laplace equation in 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. A solution to the 2-Laplace equation in a wider class of spaces is presented.

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