Stochastic two-scale convergence and Young measures

Martin Heida; Stefan Neukamm; Mario Varga

doi:10.3934/nhm.2022004

Article Contents

2022, Volume 17, Issue 2: 227-254. Doi: 10.3934/nhm.2022004

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Stochastic two-scale convergence and Young measures

1.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
2.
Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
3.
Fakultät Mathematik, Technische Universität Dresden, 01062 Dresden, Germany

^*Corresponding author: Stefan Neukamm
^*Corresponding author: Stefan Neukamm

Received: June 2021

Revised: January 2022

Early access: February 2022

Published: April 2022

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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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Mathematics Subject Classification: Primary: 74Q05, 47J30; Secondary: 49J45.

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References

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