Estimates for Elliptic Systems in a Narrow Region arising from Composite Materials

Abstract

In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises from the study of damage analysis of high-contrast composite materials. Our results show that the damage may initiate from the narrowest place.

21 pages, to appear in Quart. Appl. Math