Correctors and Field Fluctuations for the $p_ε(x)$-Laplacian with Rough Exponents: Cases$1<p_1\leq p_2\leq 2$ and $1<p_1\leq 2\leq p_2$

Details Correctors and Field Fluctuations for the $p_ε(x)$-Laplacian with Rough Exponents: Cases$1<p_1\leq p_2\leq 2$ and $1<p_1\leq 2\leq p_2$ Correctors and Field Fluctuations for the $p_ε(x)$-Laplacian with Rough Exponents: Cases$1<p_1\leq p_2\leq 2$ and $1<p_1\leq 2\leq p_2$

2011-07-15

arxiv.org/abs/1107.3181v1

Mathematics

Analysis of PDEs

Scientific paper

A corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior is provided. 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. In [7] the results of the present paper were developed for $2\leq p_1\leq p_2$, where $p_1$ and $p_2$ are the values taken by $p_{\epsilon}(x)$. In this paper the analysis focuses on the cases when $1

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