Abbasali Mohammadi, Mohsen Yousefnezhad
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.
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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