Homogenization of Hamilton-Jacobi Equations by Variational Methods
An early work on homogenization is
- (with Diogo Gomes) Computing the effective Hamiltonian using a variational approach, SIAM Journal on Control and Optimization, Volume 43 (2004) Number 3 pages 793-812.
- journal link
- ObermanGomes.pdf
- Later appeared in: Proceedings of the Joint 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05), Seville, Spain, December 12-15 (2005).
This paper uses a variational approach to homogenize a Hamilton-Jacobi equation. This paper has connections with the work of my coauthor Diogo Gomes on Mather measures.
A related work
- (with Diogo Gomes) Viscosity Solutions Methods for Converse KAM Theory, ESAIM: M2AN, Vol 42 (2008) 1047-1064.
applied the homogenization formula to detect non-integrable regions in several dynamical systems: a forced pendulum, two coupled penduli, and the double pendulum.