Preprint

Inserted: 14 apr 2025
Last Updated: 14 apr 2025

Year: 2025

Abstract:

We prove stochastic homogenization for integral functionals with integrands having p-growth, defined on Sobolev-functions taking values in a given closed $C^1$-submanifold of $\mathbb{R}^m$ without boundary. We thus extend previous results on relaxation and periodic homogenization. Our approach is flexible enough to also include the analysis of Dirichlet boundary conditions, the latter being non-trivial due to the lack of a fundamental estimate in the manifold-valued setting.

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• BR25.pdf