Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Local regularity theorems for the stationary thermistor problem

Xiangsheng Xua1

a1 Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Abstract

In this paper we present a simpler proof of a result of Lewis concerning the continuity of weak solutions to the two-dimensional thermistor problem in the case where the temperature can blow up in a region with non-empty interior. Some other regularity properties are also discussed.

(Received October 08 2003)

(Accepted March 01 2004)