Correctors and field fluctuations for the pϵ(x)-laplacian with rough exponents : The sublinear growth case

Silvia Jimenez

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 2, page 349-375
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Jimenez, Silvia. "Correctors and field fluctuations for the pϵ(x)-laplacian with rough exponents : The sublinear growth case." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 349-375. <http://eudml.org/doc/273254>.

@article{Jimenez2013,
abstract = {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.},
author = {Jimenez, Silvia},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {correctors; field concentrations; dispersed media; homogenization; layered media; p-laplacian; periodic domain; power-law materials; young measures; -Laplacian; Young measures},
language = {eng},
number = {2},
pages = {349-375},
publisher = {EDP-Sciences},
title = {Correctors and field fluctuations for the pϵ(x)-laplacian with rough exponents : The sublinear growth case},
url = {http://eudml.org/doc/273254},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Jimenez, Silvia
TI - Correctors and field fluctuations for the pϵ(x)-laplacian with rough exponents : The sublinear growth case
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 2
SP - 349
EP - 375
AB - 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.
LA - eng
KW - correctors; field concentrations; dispersed media; homogenization; layered media; p-laplacian; periodic domain; power-law materials; young measures; -Laplacian; Young measures
UR - http://eudml.org/doc/273254
ER -

References

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