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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2017

VARIATIONAL AND VISCOSITY OPERATORS FOR THE EVOLUTIVE HAMILTON-JACOBI EQUATION

Résumé

We study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax-Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable.
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Dates et versions

hal-01637617 , version 1 (29-01-2018)

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Valentine Roos. VARIATIONAL AND VISCOSITY OPERATORS FOR THE EVOLUTIVE HAMILTON-JACOBI EQUATION. Communications in Contemporary Mathematics, In press. ⟨hal-01637617⟩
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