Asymptotic behaviour for a parabolic system with nonlinear boundary conditions.
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
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...
Optimal regularity for the pseudo infinity Laplacian
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.
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...
Symmetry properties for the extremals of the Sobolev trace embedding
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...
Approximation of the Sobolev trace constant.
Large solutions for the laplacian with a power nonlinearity given by a variable exponent
Weak solutions for the -Laplacian with a nonlinear boundary condition at resonance.
Explosion time in stochastic differential equations with small diffusion.
Isolation and simplicity for the first eigenvalue of the -Laplacian with a nonlinear boundary condition.
Semilinear problems perturbed through the boundary condition
Infinitely many solutions for an elliptic system with nonlinear boundary conditions.
Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions.
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