A generic property for the eigenfunctions of the Laplacian

Antônio Luiz Pereira, Marcone Corrêa Pereira

DOI: http://dx.doi.org/10.12775/TMNA.2002.038

Abstract


In this work we show that, generically in the set of
$\mathcal{C}^2$
bounded regions of $\mathbb R^n$, $n \geq 2$, the inequality
$ \int_{\Omega} \phi^3 \neq 0$ holds for any eigenfunction
of the Laplacian with either Dirichlet or Neumann boundary conditions.

Keywords


Generic properties; boundary value problem; eigenfunction

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