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.
Titolo: | A PDE approach to nonlinear potential theory |
Autori: | Gigli, N.; Mondino, A. |
Rivista: | |
Data di pubblicazione: | 2013 |
Volume: | 100 |
Fascicolo: | 4 |
Pagina iniziale: | 505 |
Pagina finale: | 534 |
Digital Object Identifier (DOI): | 10.1016/j.matpur.2013.01.011 |
Appare nelle tipologie: | 1.1 Journal article |
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PDE-nonlinear.pdf | Post-print | Non specificato | Open Access Visualizza/Apri |
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