Stochastic homogenization of $L^{\infty }$ variational problems

Abstract

We present a homogenization result for $L^{\infty }$ variational problems in general stationary ergodic random environments. By introducing a generalized notion of distance function (a special solution of an associated eikonal equation) and demonstrating a connection to absolute minimizers of the variational problem, we obtain the homogenization result as a consequence of the fact that the latter homogenizes in random environments.

27 pages, minor changes, to appear in Adv Math

References in corpus (1)

• An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

Cited by in corpus (3)

• Geodesics of Random Riemannian Metrics
• On the first eigenpair of singularly perturbed operators with oscillating coefficients
• Geodesics of Random Riemannian Metrics: Supplementary Material