Electron. J. Differential Equations,
Vol. 2019 (2019), No. 35, pp. 113.
The pLaplace equation in a class of Hormander vector fields
Thomas Bieske, Robert D. Freeman
Abstract:
We find the fundamental solution to the pLaplace equation in a class
of Hormander vector fields that generate neither a Carnot group nor
a Grushintype space. The singularity occurs at the subRiemannian 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 pLaplace 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: pLaplacian; 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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