We show that the tools recently introduced by the first author in  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.
|Titolo:||A PDE approach to nonlinear potential theory|
|Autori:||GIGLI N; Mondino Andrea|
|Rivista:||JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES|
|Data di pubblicazione:||2013|
|Appare nelle tipologie:||1.1 Journal article|