Some properties of the principal Dirichlet eigenfunction in Lipschitz domains, via probabilistic couplings

Quentin Berger, Nicolas Bouchot

We study a discrete and continuous version of the spectral Dirichlet problem in an open bounded connected set $\hat{I}\text{c◯}\subset {\mathbb{R}}^d$, in dimension $d\ge 2$. More precisely, cons…