Optimal ground state energy of two-phase conductors

Abstract

We 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 false for all dimensions greater than or equal to two.

Keywords

• Eigenvalue optimization
• two-phase conductors
• rearrangements
• Bessel function