14 citations · 19 across the 14 of their papers we have counts for
20 papers
A unified quantitative approach to Chiti and Kohler--Jobin inequalities
Vincenzo Amato, Luca Barbato, Emanuele Cristoforoni +4
We obtain two quantitative results related to classical rearrangement inequalities for the first Dirichlet eigenvalue. The first one is a quantitative version of Chiti's reverse Hö…
The Makai inequality in higher dimensions: qualitative and quantitative aspects
Vincenzo Amato, Nunzia Gavitone, Rossano Sannipoli
In this paper, given a convex, bounded, open set we prove a sharp inequality involving the Laplacian torsional rigidity and both the perimeter and the measu…
On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions
Vincenzo Amato, Nunzia Gavitone, Francesca de Giovanni
In this paper, we study the optimization of the first Laplacian eigenvalue on axisymmetric doubly connected domains under positive Robin boundary conditions. Under additional geome…
On some functionals involving torsional rigidity, principal eigenvalue and perimeter
Vincenzo Amato, Carlo Nitsch, Cristina Trombetti +1
In this paper we study some relationships between the first Dirichlet eigenvalue and the torsional rigidity of a domain . We consider the problem of optimizing the…
A quantitative Talenti-type comparison result with Robin boundary conditions
Vincenzo Amato, Rosa Barbato, Simone Cito +2
The purpose of this paper is to establish a quantitative version of the Talenti comparison principle for solutions to the Poisson equation with Robin boundary conditions. This quan…
On the stability of the annulus for the torsion of multiply connected domains
Vincenzo Amato, Luca Barbato
We establish a quantitative version of the isoperimetric inequality for the torsion of multiply connected domains, among sets with given area and with given joint area of the holes…
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…
On the optimal sets in Pólya and Makai type inequalities
Vincenzo Amato, Nunzia Gavitone, Rossano Sannipoli
In this paper, we examine some shape functionals, introduced by Pólya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and…
A sharp quantitative nonlinear Poincaré inequality on convex domains
Vincenzo Amato, Dorin Bucur, Ilaria Fragalà
For any , we give a new inequality for the first nontrivial Neumann eigenvalue of the -Laplacian on a convex domain wi…
Quantitative comparison results for first-order Hamilton-Jacobi equations
Vincenzo Amato, Luca Barbato
In this paper, we study a quantitative refinement of a classical symmetrisation result for first-order Hamilton-Jacobi equations. We prove that the deficit in the comparison result…
The geometric size of the fundamental gap
Vincenzo Amato, Dorin Bucur, Ilaria Fragalà
The fundamental gap conjecture proved by Andrews and Clutterbuck in 2011 provides the sharp lower bound for the difference between the first two Dirichlet Laplacian eigenvalues in…
The Talenti comparison result in a quantitative form
Vincenzo Amato, Rosa Barbato, Alba Lia Masiello +1
In this paper, we obtain a quantitative version of the classical comparison result of Talenti for elliptic problems with Dirichlet boundary conditions. The key role is played by 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…
On the gradient rearrangement of functions
Vincenzo Amato, Andrea Gentile, Carlo Nitsch +1
In this paper, we introduce a symmetrization technique for the gradient of a $\BV$ function, which separates its absolutely continuous part from its singular part (sum of the jump…
Isoperimetric estimates for solutions to the p-Laplacian with variable Robin boundary conditions
Vincenzo Amato, Francesco Chiacchio, Andrea Gentile
In this paper we study the -Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we pr…
On the symmetric rearrangement of the gradient of a Sobolev function
Vincenzo Amato, Andrea Gentile
In this paper, we generalize a classical comparison result for solutions to Hamilton-Jacobi equations with Dirichlet boundary conditions, to solutions to Hamilton-Jacobi equations…
Estimates for Robin -Laplacian eigenvalues of convex sets with prescribed perimeter
Vincenzo Amato, Andrea Gentile, Alba Lia Masiello
In this paper, we prove an upper bound for the first Robin eigenvalue of the -Laplacian with a positive boundary parameter and a quantitative version of the reverse Faber-Krahn…
On the solutions to -Poisson equation with Robin boundary conditions when goes to
Vincenzo Amato, Alba Lia Masiello, Carlo Nitsch +1
We study the behaviour, when , of the first -Laplacian eigenvalues with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that th…
Sharp and quantitative estimates for the Torsion of convex sets
Vincenzo Amato, Alba Lia Masiello, Gloria Paoli +1
Let , , be a bounded, open and convex set and let be a positive and non-increasing function depending only on the distance from the boundary of $…
Comparison results for solutions to p-Laplace equations with Robin boundary conditions
Vincenzo Amato, Andrea Gentile, Alba Lia Masiello
In the last decades comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the resu…