Department of Mathematics and Statistics
University of South Florida
Tampa, FL 33620, USA
email: tbieske@mail.usf.edu
Department of Mathematics and Statistics
University of South Florida
Tampa, FL 33620, USA
email: rfreeman1@mail.usf.edu
Thomas Bieske, Robert D. Freeman
Abstract:
We find the fundamental solution to the p-Laplace equation in a class
of Hormander vector fields that generate neither a Carnot group nor
a Grushin-type space. The singularity occurs at the sub-Riemannian points,
which naturally corresponds to finding the fundamental solution of a
generalized operator in Euclidean space. We then extend these solutions
to a generalization of the p-Laplace equation and use these solutions
to find infinite harmonic functions and their generalizations.
We also compute the capacity of annuli centered at the singularity.
Submitted July 28, 2018. Published February 28, 2019.
Math Subject Classifications: 35R03, 35A08, 35C05, 53C17, 31C45, 31E05.
Key Words: p-Laplacian; Hormander vector fields; fundamental solution;
nonlinear potential theory.
Show me the PDF file (238 KB), TEX file for this article.
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Thomas J. Bieske Department of Mathematics and Statistics University of South Florida Tampa, FL 33620, USA email: tbieske@mail.usf.edu |
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Robert D. Freeman Department of Mathematics and Statistics University of South Florida Tampa, FL 33620, USA email: rfreeman1@mail.usf.edu |
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