G-闭包的局部character的变分方法：凸情形
A variational approach to the local character of G-closure: the convex case
摘要：
本文采用周期均匀化方法研究了复合材料的各种可能的有效行为。这被称为$G$闭包问题。在凸性和$p$ -增长条件（$p>1$）下，证明了由$Γ$ -收敛分析得到的所有可能的有效能量密度，都可以由具有指定体积分数的周期均匀化能量密度序列的逐点极限局部恢复.在没有任何凸性假设的情况下，给出了一个较弱的局部性结果，并利用Young测度刻画了有效能量密度的零水平集。一个类似的结果给出了细胞integrands，使提出新的反例的有效性的细胞公式在非凸的情况下，连续性的行列式关于两个尺度收敛。
英文摘要：
This article is devoted to characterize all possible effective behaviors of composite materials by means of periodic homogenization. This is known as a $G$-closure problem. Under convexity and $p$-growth conditions ($p>1$), it is proved that all such possible effective energy densities obtained by a $Γ$-convergence analysis, can be locally recovered by the pointwise limit of a sequence of periodic homogenized energy densities with prescribed volume fractions. A weaker locality result is also provided without any kind of convexity assumption and the zero level set of effective energy densities is characterized in terms of Young measures. A similar result is given for cell integrands which enables to propose new counter-examples to the validity of the cell formula in the nonconvex case and to the continuity of the determinant with respect to the two-scale convergence.
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