Gradient Estimates for the Perfect Conductivity Problem

Details Gradient Estimates for the Perfect Conductivity Problem Gradient Estimates for the Perfect Conductivity Problem

2006-12-18

arxiv.org/abs/math/0612520v1

Mathematics

Analysis of PDEs

Scientific paper

This paper concerns optimal gradient estimates of solutions for the perfect
conductivity problem with closely spaced interfacial boundaries. The problem
arises from composite material. Our estimates exhibit different blow up rates
of the gradients, as the distance between the inclusions goes to zero, in
dimensions n=2, n=3 and n\ge 4, which become higher as dimensions increase.

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