Bieske, ThomasFreeman, Robert D.2021-11-012021-11-012019-02-28Bieske, 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. 1-13.1072-6691https://hdl.handle.net/10877/14744We 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.Text13 pages1 file (.pdf)enAttribution 4.0 Internationalp-LaplacianHörmander vector fieldsFundamental solutionNonlinear potential theoryArticle