**abstract:**
Motivated by the classical "tug-of-war" game, we consider a non-local
version of the game which goes as follows: at every step two players pick
respectively a direction and then, instead of flipping a coin in order to
decide which direction to choose and then moving of a fixed amount
ϵ>0 (as is done in the classical case), it is a s-stable Levy
process which chooses at the same time both the direction and the distance to travel. Starting from this game, we heuristically we derive a
deterministic non-local integro-differential equation that we call
"infinity fractional Laplacian". We study existence, uniqueness, and
regularity, both for the Dirichlet problem and for a double obstacle
problem, both problems having a natural interpretation as "tug-of-war"
games.
In case some "randomness/unsteadiness" is added in the game, we obtain a non-local version of the p-laplacian.

Thu 5 Jul, 11:25 - 12:25, Aula Dini

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