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

collaborators

36 papers

math.SP2026

A reverse Faber--Krahn inequality for the Robin Laplacian with negative boundary parameter: small coupling in all dimensions

Nunzia Gavitone, David Krejcirik, Gloria Paoli

We establish Bareket's conjecture from 1977 for convex domains in all dimensions in the regime of weak boundary coupling. In other words, we consider the Laplace operator, subject…

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.SP2026

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…

math.OC2026

Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions

Nunzia Gavitone, David Krejcirik, Gloria Paoli

Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain $Ω \subset R^{d}$ with $d \geq 3$ , we consider the Robin-Laplacian torsional rigidity $τ_α(Ω)…

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.SP2019★ 1 cited

Efficiency and localisation for the first Dirichlet eigenfunction

Michiel van den Berg, Francesco Della Pietra, Giuseppina Di Blasio +1

Bounds are obtained for the efficiency or mean to peak ratio $E (Ω)$ for the first Dirichlet eigenfunction (positive) for open, connected sets $Ω$ with finite measure in Euclidean s…

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

A reverse Faber--Krahn inequality for the Robin Laplacian with negative boundary parameter: small coupling in all dimensions

The Makai inequality in higher dimensions: qualitative and quantitative aspects

On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions

Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions

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

Efficiency and localisation for the first Dirichlet eigenfunction

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