This paper concerns minimization and maximization of the first eigenvalue in problems involving the p-Laplacian, under homogeneous Dirichlet boundary conditions. Physically, in the case of N = 2 and p close to 2, our equation models the vibration of a nonhomogeneous membrane Ω which is fixed along the boundary. Given several materials (with different densities) of total extension |Ω|, we investigate the location of these material inside Ω so as to minimize or maximize the first mode in the vibration of the membrane.
Optimization of the first eigenvalue in problems involving the p-Laplacian
CUCCU, FABRIZIO;
2009-01-01
Abstract
This paper concerns minimization and maximization of the first eigenvalue in problems involving the p-Laplacian, under homogeneous Dirichlet boundary conditions. Physically, in the case of N = 2 and p close to 2, our equation models the vibration of a nonhomogeneous membrane Ω which is fixed along the boundary. Given several materials (with different densities) of total extension |Ω|, we investigate the location of these material inside Ω so as to minimize or maximize the first mode in the vibration of the membrane.File in questo prodotto:
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