The free material design problem for the stationary heat equation on low dimensional structure

Abstract

Abstract For a given balanced distribution of heat sources and sinks, Q, we find an optimal conductivity tensor field, C ˆ , minimizing the thermal compliance. We present C ˆ in a rather explicit form in terms of the datum. Our solution is a Borel measure taking values in a cone of non-negative tensors. We present a series of examples with explicit solutions.