Inserted: 31 mar 2009
Last Updated: 10 feb 2015
Journal: J. Math. Anal. Appl.
In this paper we prove that if $O_1$ and $O_2$ are close enough for the complementary Hausdorff distance and their boundaries satisfy some geometrical and topological conditions then the difference $
$, where $\lambda_1$ (resp. $\mu_1$) is the first Dirichlet eigenvalue of the Laplacian in $O_1$ (resp. $O_2$), is controlled by the Lebesgue measure of the symetric difference between $O_1$ and $O_2$.