an:00681105
Zbl 0808.60056
Bourgeat, Alain; Mikeli??, Andro; Wright, Steve
Stochastic two-scale convergence in the mean and applications
EN
J. Reine Angew. Math. 456, 19-51 (1994).
00022583
1994
j
60H15
stochastic homogenization; method of two-scale convergence; compactness and convergence results; monotone operators; nonlocal limits
We study stochastic homogenization of partial differential equations generalizing the method of two-scale convergence. We extend two-scale convergence from the periodic setting to the more general stochastic setting. We establish several compactness and convergence results that are important tools in the solution of homogenization problems for partial differential equations. Applying these results to several examples, we then obtain generalizations of previous results concerning classical linear problems in stochastic homogenization as well as in problems involving monotone operators and nonlocal limits. All these results are obtained with no ergodicity hypotheses on the underlying measures.
A.Bourgeat (Saint-Etienne)