Minimization of the first eigenvalue in problems involving the bi-laplacian

• Anedda, Claudia ^[1] ; Cuccu, Fabrizio ^[1] ; Porru, Giovanni ^[1]
  1. [1] Universitá di Cagliari ,Dipartimento di Matematica e Informatica
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 16, Nº. 1, 2009, págs. 127-136
• Idioma: inglés
• DOI: 10.15517/rmta.v16i1.1422
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• Resumen
  • español

    Este art´?culo trata de la minimizaci´on del primer autovalor en problemas relativosal bi-Laplaciano bajo condiciones de frontera homog´eneas de tipo Navier o Dirichlet.F´?sicamente, en el problema bi-dimensional, nuestra ecuacin modela la vibraci´on deuna placa inhomog´enea  fija con goznes a lo largo de su borde. Dados varios materiales(de diferentes densidades) y extensi´on total ||, investigamos cu´al debe serla localizaci´on de tales materiales en la placa para minimizar el primer modo de suvibraci´on.Palabras clave: bi-Laplaciano, primer autovalor, minimizaci´on.

  • English

    This paper concerns the minimization of the first eigenvalue in problems involvingthe bi-Laplacian under either homogeneous Navier boundary conditions or homogeneousDirichlet boundary conditions. Physically, in case of N = 2, our equation modelsthe vibration of a non homogeneous plate  which is either hinged or clamped alongthe boundary. Given several materials (with different densities) of total extension ||,we investigate the location of these materials inside  so to minimize the first modein the vibration of the corresponding plate.Keywords: bi-Laplacian, first eigenvalue, minimization.

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