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Recent Trends in Nonlinear Diffusion

Non-Local Gradient Dependent Operators

speaker: Alessio Figalli (ETH Zurich)

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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