WIAS Preprint No. 2885, (2021)

Stochastic two-scale convergence and Young measures


Authors

  • Heida, Martin
    ORCID: 0000-0002-7242-8175
  • Neukamm, Stefan
    ORCID: 0000-0002-8586-0661
  • Varga, Mario

2020 Mathematics Subject Classification

  • 49J40 74Q10 35K57

Keywords

  • Stochastic homogenization, unfolding, two-scale convergence, Young measures

DOI

10.20347/WIAS.PREPRINT.2885

Abstract

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 unfolding, but which cannot be treated via quenched stochastic two-scale convergence.

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