Calculus of Variations and Geometric Measure Theory

M. Bardi - G. Terrone

On the Homogenization of some Non-coercive Hamilton--Jacobi--Isaacs Equations

created by bardi on 01 Apr 2011
modified on 17 Jul 2013


Published Paper

Inserted: 1 apr 2011
Last Updated: 17 jul 2013

Journal: Comm. Pure Appl. Anal.
Volume: 12
Pages: 207--236
Year: 2013
Doi: 10.3934/cpaa.2013.12.237


We study the homogenization of Hamilton-Jacobi equations with oscillating initial data and non-coercive Hamiltonian, mostly of the Bellman-Isaacs form arising in optimal control and differential games. We describe classes of equations for which pointwise homogenization fails for some data. We prove locally uniform homogenization for various Hamiltonians with some partial coercivity and some related restrictions on the oscillating variables, mostly motivated by the applications to differential games, in particular of pursuit-evasion type. The effective initial data are computed under some assumptions of asymptotic controllability of the underlying control system with two competing players.