Homogenization of Hamilton-Jacobi Equations by Variational Methods - Adam Oberman Math

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.