Generic properties of eigenvalues of the fractional Laplacian
Fall, Mouhamed Moustapha, Marco Ghimenti, Anna Maria Micheletti, Angela Pistoia · arXiv (Cornell University) · 2023
We consider the Dirichlet eigenvalues of the fractional Laplacian $(-Δ)^s$, with $s\in (0,1)$, related to a smooth bounded domain $Ω$. We prove that there exists an arbitrarily small perturbation $\tildeΩ=(I+ψ)(Ω)$ of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian associated to $\tildeΩ$ are simple. As a consequence we obtain that all Dirichlet eigenvalues of the fractional Laplacian on an interval are simple. In addition, we prove that for a generic choice of parameters all the eigenvalues of some non-local operators are also simple.