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Maximization of the first eigenvalue in problems involving the bi-Laplacian

โœ Scribed by Fabrizio Cuccu; Giovanni Porru

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
321 KB
Volume
71
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

This paper concerns maximization of the first eigenvalue in problems involving the bi-Laplacian under either Navier boundary conditions or Dirichlet boundary conditions.

Physically, in the case of N = 2, our equation models the vibration of a nonhomogeneous plate โ„ฆ which is either hinged or clamped along the boundary. Given several materials (with different densities) of total extension |โ„ฆ|, we investigate the location of these materials throughout โ„ฆ so as to maximize the first eigenvalue in the vibration of the corresponding plate.

๐Ÿ“œ SIMILAR VOLUMES

Eigenvalues of the -Laplacian Neumann pr
Eigenvalues of the -Laplacian Neumann problems
โœ Xianling Fan ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 275 KB

We study the eigenvalues of the p(x)-Laplacian operator with zero Neumann boundary condition on a bounded domain, where p(x) is a continuous function defined on the domain with p(x) > 1. We show that, similarly to the p-Laplacian case, the smallest eigenvalue of the problem is 0 and it is simple, an