Optimal ground state energy of two-phase conductors

Abstract

Consider the problem of distributing two conducting materials in a ball with fixed proportion in order to minimize the first eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the material with the highest conductivity in a ball around the center. In this paper, we show that the conjecture is not true for all dimensions $n\ge 2$.

References in corpus (1)

• A nonlinear eigenvalue problem arising in a nanostructured quantum dot