Stochastic Homogenisation of nonconvex functionals in the space of $\mathbb{A}$-weakly differentiable maps

Autor:	Wozniak, Piotr
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	We prove the $\Gamma$-convergence of sequences of differentially constrained, random integral functionals of the form \begin{equation*} \int_{U} f\Big(\omega, x/\varepsilon, \mathbb{A} u\Big) \mathrm{d} x \end{equation*} for the class of vectorial differential operators $\mathbb{A}$ with finite-dimensional nullspaces. This work is intended to generalise results for the full gradient and to cover the cases of symmetric gradients and the deviatoric operator. The homogenisation procedure is carried out by employing a variant of the blow-up method in the setting of $\mathbb{A}$-weakly differentiable maps along with the Akcloglu-Krengel subadditive ergodic theorem. Comment: Certain arguments have to be adjusted and restructured
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.01526 Zobrazit plný text záznamu View this record from Arxiv