Electron. J. Diff. Eqns., Vol. 2004(2004), No. 114, pp. 1-21

Generic simplicity of eigenvalues for a Dirichlet problem of the bilaplacian operator

Marcone C. Pereira

Abstract:
In this work we show that the eigenvalues of the Dirichlet problem for the Bilaplacian are generically simple in the set of $C^4$-regular regions.

Submitted April 8, 2004. Published September 29, 2004.
Math Subject Classifications: 35B20, 35J40, 58D19.
Key Words: Generic properties; perturbation of the boundary; bilaplacian.

An addendum was attached on June 30, 2006. The author corrects some typing mistakes found in Section 5: The open interval $(-M,0)$ must be replaced by the closed interval $[-M,0]$ in the following definitions: $G$ in Lemma 5.3 (page 14), $Q$ in Lemma 5.4 (page 16), and $F$ in Theorem 5.5 (page 19).

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Marcone Correa Pereira
Instituto de Matemática e Estatística
Universidade de São Paulo, São Paulo, Brazil
email: marcone@ime.usp.br

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