Correctors and field fluctuations for the ${p}_{\epsilon }\left(x\right)$-laplacian with rough exponents : The sublinear growth case
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 2, p. 349-375

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.

DOI : https://doi.org/10.1051/m2an/2012030
Classification:  35J66,  35A15,  35B40,  74Q05
Keywords: correctors, field concentrations, dispersed media, homogenization, layered media, p-laplacian, periodic domain, power-law materials, young measures
@article{M2AN_2013__47_2_349_0,
author = {Jimenez, Silvia},
title = {Correctors and field fluctuations for the $p\_\varepsilon (x)$-laplacian with rough exponents : The sublinear growth case},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {47},
number = {2},
year = {2013},
pages = {349-375},
doi = {10.1051/m2an/2012030},
zbl = {1267.74095},
language = {en},
url = {http://www.numdam.org/item/M2AN_2013__47_2_349_0}
}

Jimenez, Silvia. Correctors and field fluctuations for the $p_\varepsilon (x)$-laplacian with rough exponents : The sublinear growth case. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 2, pp. 349-375. doi : 10.1051/m2an/2012030. http://www.numdam.org/item/M2AN_2013__47_2_349_0/

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