F. Chiacchio

activity

20032026

most citedA sharp lower bound for some Neumann eigenvalues of the Hermite operator

4 citations · 9 across the 26 of their papers we have counts for

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27 papers · 1 filter

math.AP2026

Kohler-Jobin inequality for $p$ -Laplace operator

Francesco Chiacchio, Vincenzo Ferone, Anna Mercaldo +1

A sharp lower bound for the first Dirichlet eigenvalue of the $p$ -laplacian is derived for sets with prescribed $p$ -torsional rigidity. The result provides an extension of the clas…

math.AP2026

Weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders

Friedemann Brock, Francesco Chiacchio, Adele Ferone +1

In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.

math.AP2026

Kohler-Jobin inequality for $p$ -Laplace operator in the Gauss space

Francesco Chiacchio, Vincenzo Ferone, Anna Mercaldo +1

A sharp lower bound for the first Dirichlet eigenvalue of the $p$ -laplacian in Gaussian space is derived for sets with prescribed generalized torsional rigidity. The result provide…

math.AP2025

Isoperimetric Bounds for Weighted Steklov Eigenvalues with Radial Weights

Friedemann Brock, Francesco Chiacchio

We study the following class of Steklov eigenvalue problems: \[ \nabla \cdot \bigl( w \nabla u \bigr) = 0 \quad \text{in } Ω, \qquad \frac{\partial u}{\partial ν} = γv u \quad \tex…

math.AP2025

On the reverse isoperimetric inequality in Gauss space

Friedemann Brock, Francesco Chiacchio

In this paper we investigate the reverse isoperimetric inequality with respect to the Gaussian measure for convex sets in $R^{2}$ . While the isoperimetric problem for the…

math.AP2022

Isoperimetric estimates for solutions to the p-Laplacian with variable Robin boundary conditions

Vincenzo Amato, Francesco Chiacchio, Andrea Gentile

In this paper we study the $p$ -Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we pr…

math.AP2022

Weighted symmetrization results for a problem with variable Robin parameter

A. Alvino, F. Chiacchio, C. Nitsch +1

By means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type ine…

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★ 1 cited

Eigenvalue Estimates for $p$ -Laplace Problems on Domains Expressed in Fermi Coordinates

Barbara Brandolini, Francesco Chiacchio, Jeffrey J. Langford

We prove explicit and sharp eigenvalue estimates for Neumann $p$ -Laplace eigenvalues in domains that admit a representation in Fermi coordinates. More precisely, if $γ$ denotes a n…

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.AP2020★ 1 cited

Sharp estimates for solutions to elliptic problems with mixed boundary conditions

A. Alvino, F. Chiacchio, C. Nitsch +1

We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on $L^{1}$ comparison) between solutions to an elliptic partial d…

math.AP2019

Some isoperimetric inequalities with respect to monomial weights

Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2

We solve a class of isoperimetric problems on $R_{+}^{2} := {(x, y) \in R^{2} : y > 0}$ with respect to monomial weights. Let $α$ and $β$ be real numbers suc…

math.AP2019

Some weighted isoperimetric problems on $R_{+}^{N}$ with stable half balls have no solutions

Friedemann Brock, Francesco Chiacchio

We show the counter-intuitive fact that some weighted isoperimetric problems on the half-space $R_{+}^{N}$ , for which half-balls centered at the origin are stable, have no…

math.AP2018

A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere

Rafael D. Benguria, Barbara Brandolini, Francesco Chiacchio

Here we prove an isoperimetric inequality for the harmonic mean of the first $N - 1$ non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemis…

math.AP2018

The isoperimetric problem for a class of non-radial weights and applications

Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2

We study a class of isoperimetric problems on $R_{+}^{N}$ where the densities of the weighted volume and weighted perimeter are given by two different non-radial function…

math.AP2018

On weighted isoperimetric inequalities with non-radial densities

Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2

We consider a class of isoperimetric problems on $R_{+}^{N}$ where the volume and the area element carry two different weights of the type $∣ x ∣^{l} x_{N}^{α}$ . We solve them in…

math.AP2017

New Pólya-Szegö-type inequalities and an alternative approach to comparison results for PDE's

Friedemann Brock, Adele Ferone, Francesco Chiacchio +1

We prove some Pólya-Szegö type inequalities which involve couples of functions and their rearrangements. Our inequalities reduce to the classical Pólya-Szegö principle when the two…

math.AP2015

An isoperimetric inequality for Gauss--like product measures

Friedemann Brock, Francesco Chiacchio, Anna Mercaldo

This paper deals with various questions related to the isoperimetic problem for smooth positive measure $d μ = φ (x) d x$ , with $x \in Ω \subset R^{N}$ . Firstly we find some neces…

math.AP2014

Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

Barbara Brandolini, Francesco Chiacchio, Antoine Henrot +1

This paper deals with the eigenvalue problem for the operator $L = - Δ - x \cdot \nabla$ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizi…

math.AP2013

A remark on the radial minimizer of the Ginzburg-Landau functional

Barbara Brandolini, Francesco Chiacchio

Denote by $E_{ε}$ the Ginzburg-Landau functional in the plane and let $u ~_{ε}$ be the radial solution to the Euler equation associated to the problem $\min \left\{E_\va…

math.AP2013★ 1 cited

Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

B. Brandolini, F. Chiacchio, C. Trombetti

In this paper we prove a sharp lower bound for the first nontrivial Neumann eigenvalue $μ_{1} (Ω)$ for the $p$ -Laplace operator in a Lipschitz, bounded domain $Ω$ in $R^{n}$ . Our estim…

math.AP2012★ 2 cited

A weighted isoperimetric inequality in a wedge

Friedemann Brock, Francesco Chiacchio, Anna Mercaldo

Let $c, k_{1}, ..., k_{N}$ be non-negative numbers, and define a measure $μ$ in the wedge $W := {x \in R^{N} : x_{i} > 0, i = 1, ..., N}$ by $dμ= e^{c|x|^2} x_1 ^{k_1}...x_N ^{k_N}…

math.AP2012★ 4 cited

A sharp lower bound for some Neumann eigenvalues of the Hermite operator

B. Brandolini, F. Chiacchio, C. Trombetti

This paper deals with the Neumann eigenvalue problem for the Hermite operator defined in a convex, possibly unbounded, planar domain $Ω$ , having one axis of symmetry passing throug…

math.AP2011

Weighted isoperimetric inequalities in cones and applications

Friedemann Brock, Francesco Chiacchio, Anna Mercaldo

This paper deals with weighted isoperimetric inequalities relative to cones of $R^{N}$ . We study the structure of measures that admit as isoperimetric sets the intersectio…

Kohler-Jobin inequality for p-Laplace operator

Weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders

Kohler-Jobin inequality for p-Laplace operator in the Gauss space

Isoperimetric Bounds for Weighted Steklov Eigenvalues with Radial Weights

On the reverse isoperimetric inequality in Gauss space

Isoperimetric estimates for solutions to the p-Laplacian with variable Robin boundary conditions

Weighted symmetrization results for a problem with variable Robin parameter

Sharp estimates for the Gaussian torsional rigidity with Robin boundary conditions

Eigenvalue Estimates for p-Laplace Problems on Domains Expressed in Fermi Coordinates

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

Sharp estimates for solutions to elliptic problems with mixed boundary conditions

Some isoperimetric inequalities with respect to monomial weights

Some weighted isoperimetric problems on R+N​ with stable half balls have no solutions

A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere

The isoperimetric problem for a class of non-radial weights and applications

On weighted isoperimetric inequalities with non-radial densities

New Pólya-Szegö-type inequalities and an alternative approach to comparison results for PDE's

An isoperimetric inequality for Gauss--like product measures

Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

A remark on the radial minimizer of the Ginzburg-Landau functional

Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

A weighted isoperimetric inequality in a wedge

A sharp lower bound for some Neumann eigenvalues of the Hermite operator

Weighted isoperimetric inequalities in cones and applications

Kohler-Jobin inequality for $p$ -Laplace operator

Kohler-Jobin inequality for $p$ -Laplace operator in the Gauss space

Eigenvalue Estimates for $p$ -Laplace Problems on Domains Expressed in Fermi Coordinates

Some weighted isoperimetric problems on $R_{+}^{N}$ with stable half balls have no solutions