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arXiv · 2304.07335

Generic properties of eigenvalues of the fractional Laplacian

Mouhamed Moustapha Fall·Marco Ghimenti·Anna Maria Micheletti·Angela Pistoia
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Abstract

We consider the Dirichlet eigenvalues of the fractional Laplacian $(-\Delta)^s$, with $s\in (0,1)$, related to a smooth bounded domain $\Omega$. We prove that there exists an arbitrarily small perturbation $\tilde\Omega=(I+\psi)(\Omega)$ of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian associated to $\tilde\Omega$ 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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Mouhamed Moustapha Fall, Marco Ghimenti, Anna Maria Micheletti, Angela Pistoia. 2023-04-14. Generic properties of eigenvalues of the fractional Laplacian. https://arxiv.org/abs/2304.07335

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