An eigenvalue problem for the biharmonic operator on Z2-symmetric regions

• Autores: Antônio L. Pereira, Marcone C. Pereira
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 2, 2008, págs. 424-442
• Idioma: inglés
• DOI: 10.1112/jlms/jdm122
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• Resumen

  • In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set of 2-symmetric regions of n, n2, with a suitable topology. To accomplish this, we combine Baire's lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225�241].