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Displaying similar documents to “On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions”

On ergodic problem for Hamilton-Jacobi-Isaacs equations

Piernicola Bettiol (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the asymptotic behavior of λ v λ as λ → 0 + , where v λ is the viscosity solution of the following Hamilton-Jacobi-Isaacs equation (infinite horizon case) λ v λ + H ( x , D v λ ) = 0 , with H ( x , p ) : = min b ∈ B max a ∈ A { - f ( x , a , b ) · p - l ( x , a , b ) } . We discuss the cases in which the state of the system is required to stay in an n -dimensional torus, called periodic boundary conditions, or in the closure of a bounded connected domain Ω ⊂ ℝ n with sufficiently smooth boundary. As far as the latter is concerned, we treat both the case...

Degenerate Eikonal equations with discontinuous refraction index

Pierpaolo Soravia (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the Dirichlet boundary value problem for eikonal type equations of ray light propagation in an inhomogeneous medium with discontinuous refraction index. We prove a comparison principle that allows us to obtain existence and uniqueness of a continuous viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize...