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Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces
Marco Michetti, Luigi Provenzano, Alessandro Savo
We consider the first eigenvalue of the magnetic Laplacian with zero magnetic field on simply connected compact surfaces and we establish isoperimetric inequalities and upper bound…
Semiclassical eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds
Luigi Provenzano, Joachim Stubbe
We exploit an identity for the gradients of Laplacian eigenfunctions on compact homogeneous Riemannian manifolds with irreducible linear isotropy group to obtain asymptotically sha…
Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential
Bruno Colbois, Luigi Provenzano, Alessandro Savo
We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of endowed with an Aharonov-Bohm potential. When the flux of the potential around…
Upper bounds for the Steklov eigenvalues of the -Laplacian
Luigi Provenzano
In this note we present upper bounds for the variational eigenvalues of the Steklov -Laplacian on domains of , . We show that for the variation…
Conformal upper bounds for the eigenvalues of the -Laplacian
Bruno Colbois, Luigi Provenzano
In this note we present upper bounds for the variational eigenvalues of the -Laplacian on smooth domains of complete -dimensional Riemannian manifolds and Neumann boundary co…
Inequalities between Dirichlet and Neumann eigenvalues of the Polyharmonic operators
Luigi Provenzano
We prove that , where () are the eigenvalues of on , , with Neumann (Dirichlet) boundary conditions.