A PDE approach to nonlinear potential theory in metric measure spaces
Metric Geometry
2019-05-08 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1209.3796,
title = {A PDE approach to nonlinear potential theory in metric measure spaces},
author = {Nicola Gigli and Andrea Mondino},
journal= {arXiv preprint arXiv:1209.3796},
year = {2019}
}