Calculus of Variations and Geometric Measure Theory

N. Gigli - A. Mondino

A PDE approach to nonlinear potential theory in metric measure spaces

created by gigli on 18 Sep 2012
modified by mondino on 20 Feb 2014


Published Paper

Inserted: 18 sep 2012
Last Updated: 20 feb 2014

Journal: Journal de Math. Pures et Appl.
Year: 2012


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.

Tags: GeMeThNES