Speaker : Mikyoung Lim (Colorado State University)
Date : 2008. 9. 30(Tue), 11:00-12:00
Place : E6-1 #2411
Title : Gradient Estimates for Solutions to the Conductivity Problem
Abstract:
We obtain upper and lower bounds on the gradient of solutions to the
conductivity problem in the case where two circular conductivity inclusions in two dimensions are very close but not touching. These bounds depend on the conductivities of the inclusions, their radii, and the distance between them. Their novelty is that they give very specific information about the blow up of the gradient as the conductivities of the inclusions degenerate. We also consider the gradient blow-up problem in the case of two spherical inclusions in the three dimensional case.