A Hamilton-Jacobi equation with measures arising in \(\Gamma \)-convergence of optimal control problems. (English) Zbl 1007.49015

Briani, Ariela

Differ. Integral Equ. 12, No. 6, 849-886 (1999).

In this paper a Hamilton-Jacobi equation with a measure in the Hamiltonian arising from the \(\Gamma \)-limit of some optimal control problems is considered. A definition of viscosity solution in this case, by adapting the method of the reparametrization of Dal Maso and Rampazzo is given.

Reviewer: Milan Konečný (Ostrava)

MSC:

49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49J45	Methods involving semicontinuity and convergence; relaxation

Keywords:

Hamilton-Jacobi equation; \(\Gamma \)-convergence; optimal control problem; viscosity solution