具有粗糙指数的$p_ε(x)$ -Laplacian的校正子和场涨落：次线性增长情形
Correctors and Field Fluctuations for the $p_ε(x)$-Laplacian with Rough Exponents: The Sublinear Growth Case
摘要：
本文给出了由两种具有不同幂律性质的材料制成的周期复合材料内部梯度场的强近似的校正理论。每种材料组分具有明显不同的指数，其出现在将梯度与通量相关联的本构定律中。校正器用于开发微结构介质内梯度场的局部奇异性强度的界限。边界是多尺度的性质，可以用来衡量所施加的宏观场的放大的微观结构。本文中的结果开发的材料具有严格的幂律指数之间的-1和零。
英文摘要：
A corrector theory for the strong approximation of gradient fields inside periodic composites made from two materials with different power law behavior is provided. Each material component has a distinctly different exponent appearing in the constitutive law relating gradient to flux. The correctors are used to develop bounds on the local singularity strength for gradient fields inside micro-structured media. The bounds are multi-scale in nature and can be used to measure the amplification of applied macroscopic fields by the microstructure. The results in this paper are developed for materials having power law exponents strictly between -1 and zero.
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