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.Comment: 29 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:0907.073