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Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. (English) Zbl 1063.35025
The 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.

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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