Stochastic homogenization of $L^\infty$ variational problems
Analysis of PDEs
2012-01-26 v3 Probability
Abstract
We present a homogenization result for 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.
Keywords
Cite
@article{arxiv.1109.2853,
title = {Stochastic homogenization of $L^\infty$ variational problems},
author = {Scott N. Armstrong and Panagiotis E. Souganidis},
journal= {arXiv preprint arXiv:1109.2853},
year = {2012}
}
Comments
27 pages, minor changes, to appear in Adv Math