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arXiv · 1707.06272

Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces

Luca Capogna·Xiaodan Zhou
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Abstract

We extend Bony's propagation of support argument \cite{Bony} to $C^1$ solutions of the non-homogeneous sub-elliptic $p-$Laplacian associated to a system of smooth vector fields satisfying H\"ormander's finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf \cite{Tolksdorf}.

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Luca Capogna, Xiaodan Zhou. 2017-07-19. Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces. https://arxiv.org/abs/1707.06272

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