Nunzia Gavitone

activity

20122026

most citedSharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators

37 citations · 164 across the 28 of their papers we have counts for

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32 papers · 1 filter

math.AP2026

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 $Ω \subset R^{n}$ we prove a sharp inequality involving the Laplacian torsional rigidity and both the perimeter and the measu…

math.AP2025

On the Serrin's problem with Robin boundary conditions

Nunzia Gavitone, Riccardo Molinarolo

Let $Ω \subset R^{N}$ , $N \geq 2$ , be an open, connected, bounded set with $C^{2}$ boundary. In this paper we consider the torsion problem with Robin boundary conditions and we s…

math.AP2025

Hessian operators, overdetermined problems, and higher order mean curvatures: symmetry and stability results

Nunzia Gavitone, Alba Lia Masiello, Gloria Paoli +1

It is well known that there is a deep connection between Serrin's symmetry result -- dealing with overdetermined problems involving the Laplacian -- and the celebrated Alexandrov's…

math.AP2024

On functionals involving the $p$ -capacity and the $q$ -torsional rigidity

Michiel van den Berg, Nunzia Gavitone

Upper bounds are obtained for the $p$ -capacity of compact sets in $R^{d}$ , with $d \geq 2$ and $1 < p < d$ . Upper and lower bounds are obtained for the product of $p$ -capacity and powers…

math.AP2024

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…

math.AP2024★ 1 cited

A sharp bound for the first Robin-Dirichlet eigenvalue

Nunzia Gavitone, Gianpaolo Piscitelli

In this paper, we study the first eigenvalue of the Laplacian on doubly connected domains when Robin and Dirichlet conditions are imposed on the outer and the inner part of the bou…

math.AP2024

On a weighted anisotropic eigenvalue problem

Nunzia Gavitone, Rossano Sannipoli

In this paper we deal with a weighted eigenvalue problem for the anisotropic $(p, q)$ -Laplacian with Dirichlet boundary conditions. We study the main properties of the first eigenva…

math.AP2022

On a Steklov-Robin eigenvalue problem

Nunzia Gavitone, Rossano Sannipoli

In this paper we study a Steklov-Robin eigenvalue problem for the Laplacian in annular domains. More precisely, we consider $Ω = Ω_{0} ∖ B_{r}$ , where $B_{r}$ is the…

math.AP2021

A monotonicity result for the first Steklov-Dirichlet Laplacian eigenvalue

Nunzia Gavitone, Gianpaolo Piscitelli

In this paper, we consider the first Steklov-Dirichlet eigenvalue of the Laplace operator in annular domain with a spherical hole. We prove a monotonicity result with respect the h…

math.AP2021

Sharp estimates for the Gaussian torsional rigidity with Robin boundary conditions

Francesco Chiacchio, Nunzia Gavitone, Carlo Nitsch +1

In this paper we provide a comparison result between the solutions to the torsion problem for the Hermite operator with Robin boundary conditions and the one of a suitable symmetri…

math.AP2021

Two inequalities for the first Robin eigenvalue of the Finsler Laplacian

Giuseppina Di Blasio, Nunzia Gavitone

Let Ωbe a bounded connected, open set of \R^n with Lipschitz boundary. Let F be a suitable norm in \R^n and let Δ_F u be the so-colled Finsler Laplacian. In this paper we prove two…

math.AP2021

The Faber-Krahn inequality for the Hermite operator with Robin boundary condition

Francesco Chiacchio, Nunzia Gavitone

In this paper we prove a Faber-Krahn type inequality for the first eigenvalue of the Hermite operator with Robin boundary condition. We prove that the optimal set is an half-space…

math.AP2021★ 16 cited

An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole

Nunzia Gavitone, Gloria Paoli, Gianpaolo Piscitelli +1

In this paper we prove the existence of a maximum for the first Steklov-Dirichlet eigenvalue in the class of convex sets with a fixed spherical hole under volume constraint. More p…

math.AP2019★ 1 cited

A quantitative Weinstock inequality

Nunzia Gavitone, Domenico Angelo La Manna, Gloria Paoli +1

The paper is devoted to the study of a quantitative Weinstock inequality in higher dimension for the first non trivial Steklov eigenvalue of Laplace operator for convex sets. The k…

math.AP2019★ 1 cited

Symmetrization with respect to mixed volumes

Francesco Della Pietra, Nunzia Gavitone, Chao Xia

In this paper we introduce new symmetrization with respect to mixed volume or anisotropic curvature integral, which generalizes the one with respect to quermassintegral due to Tale…

math.AP2018★ 3 cited

Motion of level sets by inverse anisotropic mean curvature

Francesco Della Pietra, Nunzia Gavitone, Chao Xia

In this paper we consider the weak formulation of the inverse anisotropic mean curvature flow, in the spirit of Huisken-Ilmanen. By using approximation method involving Finsler-p-L…

math.AP2018

On the first Robin eigenvalue of a class of anisotropic operators

Nunzia Gavitone, Leonardo Trani

The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$ -Laplace operator with Robin boundary condition involving a function $β$ which in…

math.AP2017

Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

Francesco Della Pietra, Giuseppina di Blasio, Nunzia Gavitone

In this paper we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue $λ_{F} (p, Ω)$ of the anisotropic $p$ -Laplacian, $1 < p < + \infty$ . Our aim…

math.AP2017

On functionals involving the torsional rigidity related to some classes of nonlinear operators

Francesco Della Pietra, Nunzia Gavitone, Serena Guarino Lo Bianco

In this paper we study optimal estimates for two functionals involving the anisotropic $p$ -torsional rigidity $T_{p} (Ω)$ , $1 < p < + \infty$ . More precisely, we study $Φ(Ω)=\frac{T_p(Ω)}{…

math.AP2017★ 19 cited

A sharp weighted anisotropic Poincaré inequality for convex domains

Francesco Della Pietra, Nunzia Gavitone, Gianpaolo Piscitelli

We prove an optimal lower bound for the best constant in a class of weighted anisotropic Poincaré inequalities

math.AP2017★ 25 cited

On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators

Francesco Della Pietra, Nunzia Gavitone, Gianpaolo Piscitelli

Let $Ω$ be a bounded open set of $R^{n}$ , $n \geq 2$ . In this paper we mainly study some properties of the second Dirichlet eigenvalue $λ_{2} (p, Ω)$ of the anisotropic $p$ -Lap…

math.AP2015

Anisotropic Hardy inequalities

Francesco Della Pietra, Giuseppina di Blasio, Nunzia Gavitone

We study some Hardy-type inequalities involving a general norm in $R^{n}$ and an anisotropic distance function to the boundary. The case of the optimality of the constants is also ad…

math.AP2015

Optimizing the first eigenvalue of some quasilinear operators with respect to the boundary conditions

Francesco Della Pietra, Nunzia Gavitone, Hynek Kovarik

We consider a class of quasilinear operators on a bounded domain $Ω \subset R^{n}$ and address the question of optimizing the first eigenvalue with respect to the boundary con…

math.AP2014

Symmetrization with respect to the anisotropic perimeter and applications

Francesco Della Pietra, Nunzia Gavitone

In this paper we introduce a new type of symmetrization, which preserves the anisotropic perimeter of the level sets of a suitable concave smooth function, in order to prove sharp…

The Makai inequality in higher dimensions: qualitative and quantitative aspects

On the Serrin's problem with Robin boundary conditions

Hessian operators, overdetermined problems, and higher order mean curvatures: symmetry and stability results

On functionals involving the p-capacity and the q-torsional rigidity

On the optimal sets in Pólya and Makai type inequalities

A sharp bound for the first Robin-Dirichlet eigenvalue

On a weighted anisotropic eigenvalue problem

On a Steklov-Robin eigenvalue problem

A monotonicity result for the first Steklov-Dirichlet Laplacian eigenvalue

Sharp estimates for the Gaussian torsional rigidity with Robin boundary conditions

Two inequalities for the first Robin eigenvalue of the Finsler Laplacian

The Faber-Krahn inequality for the Hermite operator with Robin boundary condition

An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole

A quantitative Weinstock inequality

Symmetrization with respect to mixed volumes

Motion of level sets by inverse anisotropic mean curvature

On the first Robin eigenvalue of a class of anisotropic operators

Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

On functionals involving the torsional rigidity related to some classes of nonlinear operators

A sharp weighted anisotropic Poincaré inequality for convex domains

On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators

Anisotropic Hardy inequalities

Optimizing the first eigenvalue of some quasilinear operators with respect to the boundary conditions

Symmetrization with respect to the anisotropic perimeter and applications

On functionals involving the $p$ -capacity and the $q$ -torsional rigidity