BECKMANN-TYPE PROBLEM FOR DEGENERATE HAMILTON-JACOBI EQUATIONS

Hamza Ennaji (1) , Noureddine Igbida (1) , Van Thanh Nguyen (2)

1 XLIM - XLIM
2 Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam

The aim of this note is to give a Beckmann-type problem as well as corresponding optimal mass transportation associated with a degenerate Hamilton-Jacobi equation H(x, ∇u) = 0, coupled with non-zero Dirichlet condition u = g on ∂Ω. In this article, Hamiltionian H is continuous in both arguments, coercive and convex in the second, but not enjoying any property of existence of a smooth strict sub-solution. We also provide numerical examples.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Hamza Ennaji, Noureddine Igbida, Van Thanh Nguyen. BECKMANN-TYPE PROBLEM FOR DEGENERATE HAMILTON-JACOBI EQUATIONS. 2020. ⟨hal-03020324⟩