2022
DOI: 10.3934/nhm.2022004
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Stochastic two-scale convergence and Young measures

Abstract: <p style='text-indent:20px;'>In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikelić and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale convergence (by Zhikov and Pyatnitskii). In particular, we introduce stochastic two-scale Young measures as a tool to compare mean and quenched limits. Moreover, we discuss two examples, which can be naturally analyzed via stochastic unfold… Show more

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Cited by 5 publications
(1 citation statement)
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“…The two-scale convergence method was invented by G. Nguetseng and further developed by G. Allaire. We collect here the important notions and results relevant to this paper, whose proofs can be found in [11,38,39,57]. A list of spaces used in this paper is given below.…”
Section: The Two-scale Convergence Methodsmentioning
confidence: 99%
“…The two-scale convergence method was invented by G. Nguetseng and further developed by G. Allaire. We collect here the important notions and results relevant to this paper, whose proofs can be found in [11,38,39,57]. A list of spaces used in this paper is given below.…”
Section: The Two-scale Convergence Methodsmentioning
confidence: 99%