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Correctors and field fluctuations for thepϵ(x)-Laplacian withrough exponents : The sublinear growth case

Published online by Cambridge University Press:  11 January 2013

Silvia Jimenez
Silvia Jimenez*
Affiliation:
Dept. of Mathematical Sciences, Worcester Polytechnic Institute 100 Institute Road, Worcester, 01609-2280 MA, USA.. silviajimenez@wpi.edu
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Abstract

A corrector theory for the strong approximation of gradient fields inside periodiccomposites made from two materials with different power law behavior is provided. Eachmaterial component has a distinctly different exponent appearing in the constitutive lawrelating gradient to flux. The correctors are used to develop bounds on the localsingularity strength for gradient fields inside micro-structured media. The bounds aremulti-scale in nature and can be used to measure the amplification of applied macroscopicfields by the microstructure. The results in this paper are developed for materials havingpower law exponents strictly between  −1 and zero.

Keywords

Correctorsfield concentrationsdispersed mediahomogenizationlayered mediap-Laplacianperiodic domainpower-law materialsyoung measures
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 349 - 375
Copyright
© EDP Sciences, SMAI, 2013

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