Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media.

*(English)*Zbl 1063.35025The authors study the homogenization of fully nonlinear elliptic or parabolic equation in stationary ergodic media. They prove in particular that if the nonlinearity \(F\) is stationary ergodic in the fast variable the limit problem does not contain any probabilistic variable. The methods used in the periodic or almost periodic case does not work in this case and the method used here is new and based on the investigation of the obstacle problem relative to a fully nonlinear operator.

Reviewer: Marco Biroli (Milano)

##### MSC:

35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |

35B40 | Asymptotic behavior of solutions to PDEs |

47B80 | Random linear operators |

60H25 | Random operators and equations (aspects of stochastic analysis) |

37A50 | Dynamical systems and their relations with probability theory and stochastic processes |

76M50 | Homogenization applied to problems in fluid mechanics |

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\textit{L. A. Caffarelli} et al., Commun. Pure Appl. Math. 58, No. 3, 319--361 (2005; Zbl 1063.35025)

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