Eduardo V. Teixeira
A nonlinear optimization problem in Heat conduction
(396K, AMS-TeX)

ABSTRACT.  In this paper we study the existence and geometric properties of an optimal configuration to a nonlinear
optimization problem in heat conduction. The quantity to be minimized is $\int_{\partial D} \Gamma (x,u_\mu)
d\sigma$, where $D$ is a fixed domain. A nonconstant temperature distribution is prescribed on $\partial D$ and
a volume constraint on the set where the temperature is positive is imposed. Among other regularity properties
of an optimal configuration, we prove analyticity of the free boundary.