Note on infinity-superharmonic functions.
Superharmonicity of nonlinear ground states.
The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operator Δpu = div (|∇u|p-2 ∇u) is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δp is the positive solution with boundary values zero of the equation div(|∇u|p-2 ∇u) + λ |u|p-2 u = 0 in the bounded domain Ω in the n-dimensional...
Divergence forms of the infinity-Laplacian.
The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv
Regularity of p-harmonic functions on the plane.
The Harnack inequality for -harmonic functions.
Large time behavior of solutions to a class of doubly nonlinear parabolic equations.
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point Ω, Players I and II play an -step tug-of-war game with probability , and with probability ( + = 1), a random point in the ball of radius centered at is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function . We give a detailed proof of the fact that the value...
-harmonic measure is not additive on null sets
When and the -harmonic measure on the boundary of the half plane is not additive on null sets. In fact, there are finitely many sets , ,..., in , of -harmonic measure zero, such that .
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point Ω, Players I and II play an -step tug-of-war game with probability , and with probability ( + = 1), a random point in the ball of radius centered at is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function . We give a detailed proof of the fact that the value...
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