QUASI-CONVEX HAMILTON-JACOBI EQUATIONS VIA LIMITS OF FINSLER p-LAPLACE PROBLEMS AS p → ∞

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

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam

In this paper we show that the maximal viscosity solution of a class of quasiconvex Hamilton-Jacobi equations, coupled with inequality constraints on the boundary, can be recovered by taking the limit as p → ∞ in a family of Finsler p-Laplace problems. The approach also enables us to provide an optimal solution to a Beckmann-type problem in general Finslerian setting and allows recovering a bench of known results based on the Evans-Gangbo technique.

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

Hamza Ennaji, Noureddine Igbida, Van Thanh Nguyen. QUASI-CONVEX HAMILTON-JACOBI EQUATIONS VIA LIMITS OF FINSLER p-LAPLACE PROBLEMS AS p → ∞. 2021. ⟨hal-03279460⟩