The p-Laplace equation in a class of Hörmander vector fields
Date
2019-02-28
Authors
Bieske, Thomas
Freeman, Robert D.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
p-Laplacian, Hörmander vector fields, Fundamental solution, Nonlinear potential theory
Citation
Bieske, T., & Freeman, R. D. (2019). The p-Laplace equation in a class of Hörmander vector fields. <i>Electronic Journal of Differential Equations, 2019</i>(35), pp. 1-13.
Rights
Attribution 4.0 International