论文标题
在$ \ mathbb {a} $的空间中，非凸功能的随机均质化 - 弱可分化的地图
Stochastic Homogenisation of nonconvex functionals in the space of $\mathbb{A}$-weakly differentiable maps
论文作者
论文摘要
我们证明了形式的差异约束，随机积分函数的$γ$ - 连接性\ begin {qore*} \ int_ {u} f \ big（ω，x/\ varepsilon，\ varepsilon，\ varepsilon，\ mathbbbb {a} a} a} u \ big） $ \ mathbb {a} $带有有限维nullspaces。这项工作旨在概括整个梯度的结果，并涵盖对称梯度和偏离操作员的情况。同质化过程是通过在$ \ mathbb {a} $的设置以及Akcloglu-krengel亚addive Ergodic定理的情况下采用爆炸方法的变体进行的。
We prove the $Γ$-convergence of sequences of differentially constrained, random integral functionals of the form \begin{equation*} \int_{U} f\Big(ω, 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.
