Correctors and field fluctuations for the pϵ(x)-Laplacian with rough exponents : The sublinear growth case
Dept. of Mathematical Sciences, Worcester Polytechnic Institute 100 Institute
Road, Worcester, 01609-2280 MA, USA.
Revised: 13 April 2012
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.
Mathematics Subject Classification: 35J66 / 35A15 / 35B40 / 74Q05
Key words: Correctors / field concentrations / dispersed media / homogenization / layered media / p-Laplacian / periodic domain / power-law materials / young measures
© EDP Sciences, SMAI, 2013