4 papers
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…
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 meas…
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…
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…