Luigi Provenzano

activity

20142026

most citedA reverse Faber-Krahn inequality for the magnetic Laplacian

8 citations · 21 across the 20 of their papers we have counts for

collaborators

25 papers

math.SP2026

Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms

Luigi Provenzano, Alessandro Savo

We prove a sharp Szegö-Weinberger-type inequality for balanced doubly connected domains in $S^{2}$ , $R^{2}$ and $H^{2}$ . More precisely, the first positive Neuman…

math.SP2026

Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces

Marco Michetti, Luigi Provenzano, Alessandro Savo

We consider the first eigenvalue of the magnetic Laplacian with zero magnetic field on simply connected compact surfaces and we establish isoperimetric inequalities and upper bound…

math.SP2026

On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere

Luigi Provenzano, Alessandro Savo

We prove that geodesic disks are the unique maximizers of the first positive Neumann eigenvalue among all simply connected domains in $S^{2}$ with prescribed area. We then sh…

math.DG2025

Magnetic ground states and the conformal class of a surface

Bruno Colbois, Luigi Provenzano, Alessandro Savo

On a closed, orientable Riemannian surface $Σ_{g}$ of arbitrary genus $g \geq 1$ and Riemannian metric $h$ we study the magnetic Laplacian with magnetic potential given by a harmonic…

math.SP2025

Semiclassical eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds

Luigi Provenzano, Joachim Stubbe

We exploit an identity for the gradients of Laplacian eigenfunctions on compact homogeneous Riemannian manifolds with irreducible linear isotropy group to obtain asymptotically sha…

math.SP2024★ 8 cited

A reverse Faber-Krahn inequality for the magnetic Laplacian

Bruno Colbois, Corentin Léna, Luigi Provenzano +1

We consider the first eigenvalue of the magnetic Laplacian in a bounded and simply connected planar domain, with uniform magnetic field and Neumann boundary conditions. We investig…

math.SP2023★ 1 cited

Geometry of the magnetic Steklov problem on Riemannian annuli

Luigi Provenzano, Alessandro Savo

We study the geometry of the first two eigenvalues of a magnetic Steklov problem on an annulus $Σ$ (a compact Riemannian surface with genus zero and two boundary components), the m…

math.SP2023★ 1 cited

Geometric bounds for the magnetic Neumann eigenvalues in the plane

Bruno Colbois, Corentin Léna, Luigi Provenzano +1

We consider the eigenvalues of the magnetic Laplacian on a bounded domain $Ω$ of $R^{2}$ with uniform magnetic field $β > 0$ and magnetic Neumann boundary conditions. We find u…

math.SP2022★ 1 cited

Semiclassical estimates for eigenvalue means of Laplacians on spheres

Davide Buoso, Paolo Luzzini, Luigi Provenzano +1

We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet a…

math.AP2022

The first Grushin eigenvalue on cartesian product domains

Paolo Luzzini, Luigi Provenzano, Joachim Stubbe

In this paper we consider the first eigenvalue $λ_{1} (Ω)$ of the Grushin operator $Δ_{G} := Δ_{x_{1}} + ∣ x_{1} ∣^{2 s} Δ_{x_{2}}$ with Dirichlet boundary conditions on a bounded domain $Ω$ of $\mat…

math.SP2022★ 1 cited

Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential

Bruno Colbois, Luigi Provenzano, Alessandro Savo

We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of $R^{2}$ endowed with an Aharonov-Bohm potential. When the flux of the potential around…

math.DG2021

Isoparametric foliations and the Pompeiu problem

Luigi Provenzano, Alessandro Savo

A bounded domain $Ω$ in a Riemannian manifold $M$ is said to have the Pompeiu property if the only continuous function which integrates to zero on $Ω$ and on all its congruent imag…

math.SP2021

On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set

Francesco Ferraresso, Luigi Provenzano

Let $Ω$ be a bounded domain in $R^{2}$ with smooth boundary $\partial Ω$ , and let $ω_{h}$ be the set of points in $Ω$ whose distance from the boundary is smaller than $h$ . We pr…

math.SP2021

Upper bounds for the Steklov eigenvalues of the $p$ -Laplacian

Luigi Provenzano

In this note we present upper bounds for the variational eigenvalues of the Steklov $p$ -Laplacian on domains of $R^{n}$ , $n \geq 2$ . We show that for $1 < p \leq n$ the variation…

math.SP2021★ 1 cited

On the spectral asymptotics for the buckling problem

Davide Buoso, Paolo Luzzini, Luigi Provenzano +1

We provide a direct proof of Weyl's law for the buckling eigenvalues of the biharmonic operator on a wide class of domains of $R^{d}$ including bounded Lipschitz domains. The…

math.SP2020★ 3 cited

Conformal upper bounds for the eigenvalues of the $p$ -Laplacian

Bruno Colbois, Luigi Provenzano

In this note we present upper bounds for the variational eigenvalues of the $p$ -Laplacian on smooth domains of complete $n$ -dimensional Riemannian manifolds and Neumann boundary co…

math.SP2019

Inequalities between Dirichlet and Neumann eigenvalues of the Polyharmonic operators

Luigi Provenzano

We prove that $μ_{k + m}^{m} < λ_{k}^{m}$ , where $μ_{k}^{m}$ ( $λ_{k}^{m}$ ) are the eigenvalues of $(- Δ)^{m}$ on $Ω \subset R^{d}$ , $d \geq 2$ , with Neumann (Dirichlet) boundary conditions.

math.SP2019★ 1 cited

Neumann eigenvalues of the biharmonic operator on domains: geometric bounds and related results

Bruno Colbois, Luigi Provenzano

We study an eigenvalue problem for the biharmonic operator with Neumann boundary conditions on domains of Riemannian manifolds. We discuss the weak formulation and the classical bo…

math.SP2019★ 3 cited

Semiclassical bounds for spectra of biharmonic operators

Davide Buoso, Luigi Provenzano, Joachim Stubbe

We provide complementary semiclassical bounds for the Riesz means $R_{1} (z)$ of the eigenvalues of various biharmonic operators, with a second term in the expected power of $z$ . The…

math.SP2018

Complementary asymptotically sharp estimates for eigenvalue means of Laplacians

Evans M. Harrell, Luigi Provenzano, Joachim Stubbe

We present asymptotically sharp inequalities, containing a second term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the famil…

math.SP2017

Eigenvalues of elliptic operators with density

Bruno Colbois, Luigi Provenzano

We consider eigenvalue problems for elliptic operators of arbitrary order $2 m$ subject to Neumann boundary conditions on bounded domains of the Euclidean $N$ -dimensional space. We…

math.SP2016

Weyl-type bounds for Steklov eigenvalues

Luigi Provenzano, Joachim Stubbe

We present upper and lower bounds for Steklov eigenvalues for domains in $R^{N + 1}$ with $C^{2}$ boundary compatible with the Weyl asymptotics. In particular, we obtain sharp…

math.SP2016

On the stability of some isoperimetric inequalities for the fundamental tones of free plates

Davide Buoso, L. Mercredi Chasman, Luigi Provenzano

We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chas…

math.OC2015

A few shape optimization results for a biharmonic Steklov problem

Davide Buoso, Luigi Provenzano

We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type for…

Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms

Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces

On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere

Magnetic ground states and the conformal class of a surface

Semiclassical eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds

A reverse Faber-Krahn inequality for the magnetic Laplacian

Geometry of the magnetic Steklov problem on Riemannian annuli

Geometric bounds for the magnetic Neumann eigenvalues in the plane

Semiclassical estimates for eigenvalue means of Laplacians on spheres

The first Grushin eigenvalue on cartesian product domains

Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential

Isoparametric foliations and the Pompeiu problem

On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set

Upper bounds for the Steklov eigenvalues of the p-Laplacian

On the spectral asymptotics for the buckling problem

Conformal upper bounds for the eigenvalues of the p-Laplacian

Inequalities between Dirichlet and Neumann eigenvalues of the Polyharmonic operators

Neumann eigenvalues of the biharmonic operator on domains: geometric bounds and related results

Semiclassical bounds for spectra of biharmonic operators

Complementary asymptotically sharp estimates for eigenvalue means of Laplacians

Eigenvalues of elliptic operators with density

Weyl-type bounds for Steklov eigenvalues

On the stability of some isoperimetric inequalities for the fundamental tones of free plates

A few shape optimization results for a biharmonic Steklov problem

Upper bounds for the Steklov eigenvalues of the $p$ -Laplacian

Conformal upper bounds for the eigenvalues of the $p$ -Laplacian