Stochastic homogenization of $L^\infty$ variational problems

Details Stochastic homogenization of $L^\infty$ variational problems Stochastic homogenization of $L^\infty$ variational problems

2011-09-13

arxiv.org/abs/1109.2853v3

Mathematics

Analysis of PDEs

27 pages, minor changes, to appear in Adv Math

Scientific paper

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.

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