Type of Document	Dissertation
Author	Jiménez , Silvia
Author's Email Address	silvia.jimenez.bolanos@gmail.com
URN	etd-06182010-104212
Title	Homogenization of Nonlinear Partial Differential Equations
Degree	Doctor of Philosophy (Ph.D.)
Department	Mathematics
Advisory Committee	Advisor Name Title Lipton, Robert Committee Chair Adkins, William Committee Member Litherland, Richard Committee Member Sengupta, Ambar Committee Member Shipman, Stephen Committee Member Vaidyanathan, Ramachandran Dean's Representative
Keywords	p-Laplacian power law homogenization correctors layered media dispersed media periodic domain
Date of Defense	2010-05-04
Availability	unrestricted
Abstract This dissertation is concerned with properties of local fields inside composites made from two materials with different power law behavior. This simple constitutive model is frequently used to describe several phenomena ranging from plasticity to optical nonlinearities in dielectric media. We provide the corrector theory for the strong approximation of fields inside composites made from two power law materials with different exponents. The correctors are used to develop bounds on the local singularity strength for gradient fields inside microstructured media. The bounds are multiscale in nature and can be used to measure the amplification of applied macroscopic fields by the microstructure. These results are shown to hold for finely mixed periodic dispersions of inclusions and for layers.
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