Sharp stability of higher order Dirichlet eigenvalues

par Mickaël Nahon

lundi 12 déc. 2022, 10:00 → 11:00 Europe/Paris

3L15

Let $\Omega\subset\mathbb{R}^n$ be an open set with same area as the unit ball $B$ and call $\lambda_k(\Omega)$ the $k$-th eigenvalue of the Laplacian with Dirichlet condition on $\Omega$. Suppose $\lambda_1(\Omega)-\lambda_1(B)$ is small, how large can $|\lambda_k(\Omega)-\lambda_k(B)|$ be ? We establish bounds with sharp exponents depending on the multiplicity of $\lambda_k(B)$ through the study of a perturbed shape optimization problem.

This is joint work with Dorin Bucur, Jimmy Lamboley and Raphaël Prunier.