Displaying similar documents to “Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities”

Geometric constraints on the domain for a class of minimum problems

Graziano Crasta, Annalisa Malusa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider minimization problems of the form min u ∈ ϕ + W 0 1 , 1 ( Ω ) ∫ Ω [ f ( D u ( x ) ) - u ( x ) ] d x where Ω ⊆ ℝ N is a bounded convex open set, and the Borel function f : ℝ N → [ 0 , + ∞ ] is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of and the zero level set of , we prove that the viscosity solution of a related Hamilton–Jacobi equation provides a minimizer for the integral functional.

Approximation of viscosity solution by morphological filters

Denis Pasquignon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider in ℝ 2 all curvature equation ∂ u ∂ t = | D u | G ( curv ( u ) ) where is a nondecreasing function and curv() is the curvature of the level line passing by . These equations are invariant with respect to any contrast change , with nondecreasing. Consider the contrast invariant operator T t : u o → u ( t ) . A Matheron theorem asserts that all contrast invariant operator can be put in a form ( T u ) ( 𝐱 ) = inf B ∈ ℬ sup 𝐲 ∈ B u ( 𝐱 + 𝐲 ) . We show the asymptotic equivalence of both formulations. More precisely, we show that all curvature equations can be obtained...