Generic properties of eigenvalues of the fractional Laplacian

2023/04/14 by Fall, Mouhamed Moustapha, Ghimenti, Marco, Micheletti, Anna Maria +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.07335

Abstract

We consider the Dirichlet eigenvalues of the fractional Laplacian (-Δ)^s, with s∈ (0,1), related to a smooth bounded domain Ω. We prove that there exists an arbitrarily small perturbation Ω=(I+ψ)(Ω) of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian associated to Ω 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.

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