A PDE approach to nonlinear potential theory in metric measure spaces

We show that the tools recently introduced by the first author in [9] (2012) 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 sub-minimizer with a convex and non-decreasing function is again a sub-minimizer, and the third is the fact that the Busemann function associated to a line is harmonic on infinitesimally Hilbertian CD(0, N) spaces. (C) 2013 Elsevier Masson SAS. All rights reserved.