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arXiv · 1209.3796

A PDE approach to nonlinear potential theory in metric measure spaces

Nicola Gigli·Andrea Mondino
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Abstract

We show that the tools recently introduced by the first author in [9] allow to give a PDE description of p-harmonic functions in metric measure setting. Three applications are given: the first is about new results on the sheaf property of harmonic functions, the second is a PDE proof of the fact that the composition of a subminimizer with a convex and non-decreasing function is again a subminimizer, and the third is the fact that the Busemann function associated to a line is harmonic on infinitesimally Hilbertian CD(0,N) spaces.

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Nicola Gigli, Andrea Mondino. 2012-09-17. A PDE approach to nonlinear potential theory in metric measure spaces. https://doi.org/10.1016/j.matpur.2013.01.011

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