Gradient estimates for the conductivity problems and the systems of elasticity:

We investigate the high stress concentration in stiff fiber-reinforced composites. By the anti-plane shear model, this problem can be transferred into the conductivity problems with multiple inclusions. Here we consider the extreme cases, i.e. the perfect and insulated conductivity problems. We obtain the optimal blow-up rates of the gradient in the perfect conductivity problems and an upper bound of the gradient in the insulated conductivity problems. We also study the related problems in elliptic systems including systems of elasticity and obtain some partial results.Ph.D.Includes bibliographical references (p. 84-85)by Biao Yi