An eigenvalue problem for the biharmonic operator on ℤ2‐symmetric regions
Antônio Luíz Pereira, Marcone Corrêa Pereira · Journal of the London Mathematical Society · 2008
Abstract In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set of ℤ2‐symmetric regions of ℝn, n⩾2, 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].