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.
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 }, pages = {349--375}, publisher = {EDP-Sciences}, volume = {47}, number = {2}, year = {2013}, doi = {10.1051/m2an/2012030}, zbl = {1267.74095}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2012030/} }
TY - JOUR AU - Jimenez, Silvia TI - Correctors and field fluctuations for the $p_\varepsilon (x)$-laplacian with rough exponents : The sublinear growth case JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 349 EP - 375 VL - 47 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012030/ DO - 10.1051/m2an/2012030 LA - en ID - M2AN_2013__47_2_349_0 ER -
%0 Journal Article %A Jimenez, Silvia %T Correctors and field fluctuations for the $p_\varepsilon (x)$-laplacian with rough exponents : The sublinear growth case %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 349-375 %V 47 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012030/ %R 10.1051/m2an/2012030 %G en %F 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 , Volume 47 (2013) no. 2, pp. 349-375. doi : 10.1051/m2an/2012030. http://www.numdam.org/articles/10.1051/m2an/2012030/
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