A characterization of optimal two-phase multifunctional composite designs
Luís Silvestre · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2007
We study the problem of optimal design of a two-phase composite material to maximize the sum of thermal and electrical conductivity. We obtain a characterization of an optimal configuration in terms of a free boundary type H problem. In the process of obtaining this result, we provide a new proof of the relevant case of Bergman's cross-property bound. We use our characterization to argue that the optimal interface is not, as has been suggested, a periodic minimal surface.