Electron. J. Diff. Equ., Vol. 2014 (2014), No. 171, pp. 1-8.

Optimal ground state energy of two-phase conductors

Abbasali Mohammadi, Mohsen Yousefnezhad

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.

Submitted May 5, 2014. Published August 11, 2014.
Math Subject Classifications: 49Q10, 35Q93, 35P15, 33C10.
Key Words: Eigenvalue optimization; two-phase conductors; rearrangements; Bessel function.

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Abbasali Mohammadi
Department of Mathematics, College of Sciences
Yasouj University, Yasouj 75918-74934, Iran
email: mohammadi@yu.ac.ir
Mohsen Yousefnezhad
Department of Mathematical Sciences
Sharif University of Technology, Tehran, Iran
email: yousefnezhad@mehr.sharif.ir

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