Solutions of Nonlinear PDES in the Sense of Averages
نویسندگان
چکیده
We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all p′s. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 < p <∞. Résumé On charactérise les fonctions p-harmoniques, y compris les cas p = 1 at p =∞, en utilisant des propriétés de la moyenne. Ces résultats prolongenent le cas classique linéaire (p=2) du à Privaloff, à toutes les valeurs de p. Pour tout p dans l’intervalle (1,∞), on décrit une classe de jeux aléatoires de type “tug-ofwar” dont les fonctions valeur approchent le fonctions p-harmoniques lorsque le pas tend vers zero.
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