The 𝑃-Laplace equation on a class of Grushin-type spaces
Author:
Abstract
We find the fundamental solution to the P 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.
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
http://www.ams.org/proc/2006-134-12/S0002-9939-06-08394-8/S0002-9939-06-08394-8.pdf
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