Stochastic homogenization of $L^\infty$ variational problems

Scott N. Armstrong; Panagiotis E. Souganidis

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arXiv · 1109.2853

Stochastic homogenization of $L^\infty$ variational problems

Scott N. Armstrong·Panagiotis E. Souganidis

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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.

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Scott N. Armstrong, Panagiotis E. Souganidis. 2012-01-25. Stochastic homogenization of $L^\infty$ variational problems. https://arxiv.org/abs/1109.2853

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