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.
A PDE approach to nonlinear potential theory / Gigli, Nicola; Mondino, Andrea. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 100:4(2013), pp. 505-534. [10.1016/j.matpur.2013.01.011]
A PDE approach to nonlinear potential theory
Gigli, Nicola;Mondino, Andrea
2013-01-01
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.| File | Dimensione | Formato | |
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