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arXiv · 1706.09214

Green's identities, comparison principle and uniqueness of positive solutions for nonlinear $p$-sub-Laplacian equations on stratified Lie groups

Michael Ruzhansky·Durvudkhan Suragan
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Abstract

We propose analogues of Green's and Picone's identities for the $p$-sub-Laplacian on stratified Lie groups. In particular, these imply a generalised D\'iaz-Sa\'a inequality for the $p$-sub-Laplacian on stratified Lie groups. Using these we derive a comparison principle and uniqueness of a positive solution to nonlinear hypoelliptic equations on general stratified Lie groups extending to the setting of the general stratified Lie groups previously known results on Euclidean and Heisenberg groups.

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Michael Ruzhansky, Durvudkhan Suragan. 2017-06-28. Green's identities, comparison principle and uniqueness of positive solutions for nonlinear $p$-sub-Laplacian equations on stratified Lie groups. https://arxiv.org/abs/1706.09214

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