Geodesic
Optimal ground state energy of two-phase conductors
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 49Q10, 35Q93, 35P15, 33C10
Keywords: eigenvalue optimization, two-phase conductors, rearrangements, Bessel function 
@article{EJDE_2014__2014__a18,
     author = {Mohammadi,  Abbasali and Yousefnezhad,  Mohsen},
     title = {Optimal ground state energy of two-phase conductors},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1296.49044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a18/}
}
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Mohammadi,  Abbasali; Yousefnezhad,  Mohsen. Optimal ground state energy of two-phase conductors. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a18/