We consider the Dirichlet eigenvalues of the fractional Laplacian, related to a smooth bounded domain. We prove that there exists an arbitrarily small perturbation of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian 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.
Generic properties of eigenvalues of the fractional Laplacian
Ghimenti M.;Micheletti A. M.;
2023-01-01
Abstract
We consider the Dirichlet eigenvalues of the fractional Laplacian, related to a smooth bounded domain. We prove that there exists an arbitrarily small perturbation of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian 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.File in questo prodotto:
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