Recent zbMATH articles by "Pistoia, Angela"https://zbmath.org/atom/ai/pistoia.angela2024-03-13T18:33:02.981707ZWerkzeugGeneric properties of eigenvalues of the fractional Laplacianhttps://zbmath.org/1528.350302024-03-13T18:33:02.981707Z"Fall, Mouhamed Moustapha"https://zbmath.org/authors/?q=ai:fall.mouhamed-moustapha"Ghimenti, Marco"https://zbmath.org/authors/?q=ai:ghimenti.marco-g"Micheletti, Anna Maria"https://zbmath.org/authors/?q=ai:micheletti.anna-maria"Pistoia, Angela"https://zbmath.org/authors/?q=ai:pistoia.angelaIn this study, the authors investigate the Dirichlet eigenvalue problem concerning fractional powers of the Laplacian (\(\left(\Delta\right)^s\), where \(s \in (0,1)\)) within a smooth bounded domain \(\Omega\). They establish the existence of a minimal perturbation to \(\Omega\), rendering all Dirichlet eigenvalues of the fractional Laplacian powers associated with the perturbation to be simple. This leads to the conclusion that all Dirichlet eigenvalues of the fractional Laplacian powers within an interval are simple. Furthermore, the authors demonstrate that under a typical parameter selection, all eigenvalues of certain non-local operators are also distinct.
Reviewer: Nelson Vieira (Aveiro)