## 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.

Original language | English (US) |
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Pages (from-to) | 3508-3535 |

Number of pages | 28 |

Journal | Advances in Mathematics |

Volume | 229 |

Issue number | 6 |

DOIs | |

State | Published - Apr 1 2012 |

## Keywords

- Eikonal equation
- Hamilton-Jacobi equation
- L calculus of variations
- Stochastic homogenization

## ASJC Scopus subject areas

- Mathematics(all)

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