The p-Laplace equation in a class of Hörmander vector fields
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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.
CitationBieske, T., & Freeman, R. D. (2019). The p-Laplace equation in a class of Hörmander vector fields. Electronic Journal of Differential Equations, 2019(35), pp. 1-13.
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