HAMILTON-JACOBI EQUATIONS ON GRAPHS AND APPLICATIONS

Yan Shu (1)

1 MODAL'X - Modélisation aléatoire de Paris X

This paper introduces a notion of gradient and an inmal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity of this class of inmal-convolution operators is connected to some discrete version of the log-Sobolev inequality and to a discrete version of Talagrand's transport inequality.

Domaines: Analyse fonctionnelle [math.FA]

Yan Shu. HAMILTON-JACOBI EQUATIONS ON GRAPHS AND APPLICATIONS. 2014. ⟨hal-01097744v2⟩