6 papers
On the buckling eigenvalue of unbounded cylinders
Paolo Acampora, Emanuele Cristoforoni, Carlo Nitsch +1
We variationally characterize the bottom of the spectrum of the buckling problem in an infinite cylinder , where is an open bounded subset of $\mathbb{…
Sharp quantitative Talenti's inequality in particular cases
Paolo Acampora, Jimmy Lamboley
In this paper, we focus on the famous Talenti's symmetrization inequality, more precisely its corollary asserting that the -norm of the solution to is hi…
An improved version of a spectral inequality by Payne
Paolo Acampora, Emanuele Cristoforoni, Carlo Nitsch +1
A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a qu…
Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains
Paolo Acampora, Vincenzo Amato, Emanuele Cristoforoni
We investigate the relationship between the Neumann and Steklov principal eigenvalues emerging from the study of collapsing convex domains in . Such a relationship al…
A spectral isoperimetric inequality on the n-sphere for the Robin-Laplacian with negative boundary parameter
Paolo Acampora, Antonio Celentano, Emanuele Cristoforoni +2
For every given , we study the problem of maximizing the first Robin eigenvalue of the Laplacian among convex (not necessarily smooth) sets $Ω\subset\mathbb{S}^{…
On the asymptotic behavior of a diffraction problem with a thin layer
Paolo Acampora, Emanuele Cristoforoni
We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set and a thin layer locally described by , where $…