### Approximation of the Sobolev trace constant.

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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article...

In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.

We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point

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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