Calculus of Variations and Geometric Measure Theory

A. Lemenant - E. Milakis

Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in R^N

created by lemenant on 31 Mar 2009
modified on 10 Feb 2015


Published Paper

Inserted: 31 mar 2009
Last Updated: 10 feb 2015

Journal: J. Math. Anal. Appl.
Year: 2010


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 $O_2$.