@article{b8dfe0ab14774c56a3f085841b5f2a74,
title = "Stochastic homogenization of L ∞ variational problems",
abstract = "We present a homogenization result for L ∞ 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 = "Eikonal equation, Hamilton-Jacobi equation, L calculus of variations, Stochastic homogenization",
author = "Armstrong, {Scott N.} and Souganidis, {Panagiotis E.}",
note = "Funding Information: * Corresponding author. E-mail addresses: armstron@math.wisc.edu (S.N. Armstrong), souganidis@math.uchicago.edu (P.E. Souganidis). 1 Partially supported by NSF Grant DMS-1004645. 2 Partially supported by NSF Grant DMS-0901802. Funding Information: The first author was partially supported by NSF Grant DMS-1004645 and the second author by NSF Grant DMS-0901802. The first author also thanks Charlie Smart and Vesa Julin for helpful conversations. We acknowledge an anonymous referee for suggesting the example at the end of Section 5.",
year = "2012",
month = apr,
day = "1",
doi = "10.1016/j.aim.2012.02.018",
language = "English (US)",
volume = "229",
pages = "3508--3535",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "6",
}