7 papers
On some functionals for which the ball is a saddle shape
Alba Lia Masiello, Gloria Paoli, Francesco Salerno
In the present paper, we study the maximization problem of the -Torsional rigidity under quermassintegral constraint, with particular emphasis on the role of the ball. Our main…
Local stability for a class of Saint-Venant type inequalities
Luca Barbato, Francesco Salerno
We establish a local stability result for a class of Saint-Venant type inequalities. Given the solution of the Dirichlet torsion problem in a domain , we consider shape func…
Remarks on Brunn-Minkowski-type inequalities related to the Ornstein-Uhlenbeck operator
Francisco Marín Sola, Francesco Salerno
We investigate Brunn-Minkowski-type inequalities for the torsional rigidity and the first eigenvalue associated with the Ornstein-Uhlenbeck operator. Counterexamples ar…
Sharp lower bound for the Monge-Ampère torsion on convex sets
Francesco Salerno
The \emph{Monge-Ampère} torsion deficit of an open, bounded convex set of class is the normalized gap between the value of the torsion functional evaluated on…
Some shape functionals for the -Hessian equation
Alba Lia Masiello, Francesco Salerno
For a non-empty, bounded, open, and convex set of class , we consider the Torsional Rigidity associated to the -Hessian operator. We first prove Pólya type lower bound for…
Talenti comparison results for solutions to -Laplace equation on multiply connected domains
Luca Barbato, Francesco Salerno
In the last years comparison results of Talenti type for Elliptic Problems have been widely investigated. In this paper we obtain a comparison result for the -Laplace operator i…
A quantitative result for the -Hessian equation
Alba Lia Masiello, Francesco Salerno
In this paper, we study a symmetrization that preserves the mixed volume of the sublevel sets of a convex function, under which, a Pólya-Szeg\H o type inequality holds. We refine t…