6 papers · 1 filter
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{…
On the classical Reinforcement problem and Optimisation
Emanuele Cristoforoni, Carlo Nitsch, Cristina Trombetti
In the present survey, we consider the classical reinforcement problem for elliptic boundary value problems originally studied by Sanchez-Palencia in 1969. We focus on the seminar…
On the second eigenvalue of the infinity Laplacian with Robin boundary conditions
Vincenzo Amato, Alba Lia Masiello, Carlo Nitsch +1
We study the behaviour, as , of the second eigenvalues of the -Laplacian with Robin boundary conditions and the limit of the associated eigenfunctions. We prove t…
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…
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}^{…
A Talenti comparison result for a class of Neumann boundary value problems
Antonio Celentano, Carlo Nitsch, Cristina Trombetti
In this paper, we establish a comparison principle in terms of Lorentz norms and point-wise inequalities between a positive solution to the Poisson equation with non-homogeneou…