Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-temporal media
Russell W. Schwab · Indiana University Mathematics Journal · 2009
This paper considers the problem of homogeniza- tion of a class of convex Hamilton-Jacobi equations in spatio-temporal stationary ergodic environments. Special attention is placed on the interplay between the use of the Subadditive Ergodic Theorem and continuity estimates for the solutions that are independent of the oscillations in the equation. Moreover, an inf-sup formula for the effective Hamiltonian is provided.