Optimization of the first eigenvalue in problems involving the 𝑝-Laplacian

Cuccu, Fabrizio; Emamizadeh, Behrouz; Porru, Giovanni

doi:10.1090/S0002-9939-08-09769-4

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ISSN 1088-6826(online) ISSN 0002-9939(print)

Optimization of the first eigenvalue in problems involving the -Laplacian

Authors: Fabrizio Cuccu, Behrouz Emamizadeh and Giovanni Porru
Journal: Proc. Amer. Math. Soc. 137 (2009), 1677-1687
MSC (2000): Primary 35P15, 47A75
Posted: December 11, 2008
MathSciNet review: 2470826
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Abstract: This paper concerns minimization and maximization of the first eigenvalue in problems involving the -Laplacian, under homogeneous Dirichlet boundary conditions. Physically, in the case of and close to , our equation models the vibration of a nonhomogeneous membrane $\Omega$ which is fixed along the boundary. Given several materials (with different densities) of total extension $\vert\Omega\vert$ , we investigate the location of these material inside $\Omega$ so as to minimize or maximize the first mode in the vibration of the membrane.

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