Electron. J. Differential Equations, Vol. 2019 (2019), No. 35, pp. 1-13.

The p-Laplace equation in a class of Hormander vector fields

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.

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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
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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