Francesco Della Pietra

activity

20122026

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

37 citations · 178 across the 19 of their papers we have counts for

collaborators

26 papers

math.AP2026

Asymptotic behavior of the first Robin eigenvalue of nonlinear operators

Rosa Barbato, Francesco Della Pietra, Alba Lia Masiello

Let $Ω$ be a bounded Lipschitz domain of $R^{N}$ , $N \geq 2$ . In this paper, we study the asymptotic behavior of the first Robin eigenvalue of the $p$ -Laplace operator as $β$ …

math.AP2024

Pólya-type estimates for the first Robin eigenvalue of elliptic operators

F. Della Pietra

The aim of this paper is to obtain optimal estimates for the first Robin eigenvalue of the anisotropic $p$ -Laplace operator, namely: \[ λ_F(β,Ω)=λ_{F}(p,β,Ω)= \min_{ψ\in W^{1,p}(Ω)…

math.AP2023

On a nonlinear Robin problem with an absorption term on the boundary and $L^{1}$ data

Francesco Della Pietra, Francescantonio Oliva, Sergio Segura de León

We deal with existence and uniqueness of nonnegative solutions to \begin{equation*} \left\{ \begin{array}{l} -Δu = f(x) \text{ in }Ω, \frac{\partial u}{\partial ν} + λ(x) u = \frac…

math.AP2023★ 3 cited

On the first Robin eigenvalue of the Finsler $p$ -Laplace operator as $p \to 1$

Rosa Barbato, Francesco Della Pietra, Gianpaolo Piscitelli

Let $Ω$ be a bounded, connected, sufficiently smooth open set, $p > 1$ and $β \in R$ . In this paper, we study the $Γ$ -convergence, as $p \to 1^{+}$ , of the functional \[ J…

math.AP2022

Behaviour of solutions to $p$ -Laplacian with Robin boundary conditions as $p$ goes to $1$

Francesco Della Pietra, Francescantonio Oliva, Sergio Segura de León

We study the asymptotic behaviour, as $p \to 1^{+}$ , of the solutions of the following inhomogeneous Robin boundary value problem: \begin{equation} \label{pbabstract} \tag{P} \left\…

math.AP2022★ 9 cited

Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators

Francesco Della Pietra, Gianpaolo Piscitelli

The aim of this paper is to obtain optimal estimates for the first Robin eigenvalue of the anisotropic $p$ -Laplace operator, namely: \begin{equation*} λ_1(β,Ω)=\min_{ψ\in W^{1,p}(Ω…

math.AP2020★ 20 cited

An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes

Francesco Della Pietra, Gianpaolo Piscitelli

In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analo…

math.AP2020

An optimal insulation problem

Francesco Della Pietra, Carlo Nitsch, Cristina Trombetti

In this paper we consider a minimization problem which arises from thermal insulation. A compact connected set $K$ , which represents a conductor of constant temperature, say $1$ , i…

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★ 3 cited

Saturation phenomena for some classes of nonlinear nonlocal eigenvalue problems

Francesco Della Pietra, Gianpaolo Piscitelli

Let us consider the following minimum problem \[ λ_α(p,r)= \min_{\substack{u\in W_{0}^{1,p}(-1,1)\\ u\not\equiv0}}\dfrac{\displaystyle\int_{-1}^{1}|u'|^{p}dx+α\left|\int_{-1}^{1}|u…

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.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.AP2016

A saturation phenomenon for a nonlinear nonlocal eigenvalue problem

Francesco Della Pietra, Gianpaolo Piscitelli

Given $1 \leq q \leq 2$ and $α \in R$ , we study the properties of the solutions of the minimum problem \[ λ(α,q)=\min\left\{\dfrac{\displaystyle\int_{-1}^{1}|u'|^{2}dx+α\left|\i…

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…

math.AP2014

Some remarks on a shape optimization problem

Francesco Della Pietra

Given $Ω$ bounded open set of $R^{n}$ and $α \in R$ , let us consider \[ μ(Ω,α)=\min_{\substack{v\in W_{0}^{1,2}(Ω)\\v\not\equiv 0}} \frac{\displaystyle\int_Ω |\nabla…

math.AP2014

Sharp estimates and existence for anisotropic elliptic problems with general growth in the gradient

Francesco Della Pietra, Nunzia Gavitone

In this paper, we prove sharp estimates and existence results for anisotropic nonlinear elliptic problems with lower order terms depending on the gradient. Our prototype is: $ \lef…

math.AP2013★ 2 cited

Faber-Krahn inequality for anisotropic eigenvalue problems with Robin boundary conditions

Francesco Della Pietra, Nunzia Gavitone

In this paper we study the main properties of the first eigenvalue and its eigenfunctions of a class of highly nonlinear elliptic operators in a bounded Lipschitz domain, assuming…

math.OC2013

Symmetry breaking in a constrained Cheeger type isoperimetric inequality

Barbara Brandolini, Francesco Della Pietra, Carlo Nitsch +1

We study the optimal constant in a Sobolev inequality for BV functions with zero mean value and vanishing outside a bounded open set. We are interested in finding the best possible…

math.AP2013★ 10 cited

Stability results for some fully nonlinear eigenvalue estimates

Francesco Della Pietra, Nunzia Gavitone

In this paper, we give some stability estimates for the Faber-Krahn inequality relative to the eigenvalues of Hessian operators

math.AP2012★ 37 cited

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

Francesco Della Pietra, Nunzia Gavitone

We prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the p-Laplace and the pseudo-p-Laplace operators. Moreover…

math.AP2012★ 27 cited

Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials

Francesco Della Pietra, Nunzia Gavitone

We give existence and regularity results for solutions of some nonlinear elliptic problems. The equations we deal with are modeled on a problem which involves in its principal part…

Asymptotic behavior of the first Robin eigenvalue of nonlinear operators

Pólya-type estimates for the first Robin eigenvalue of elliptic operators

On a nonlinear Robin problem with an absorption term on the boundary and L1 data

On the first Robin eigenvalue of the Finsler p-Laplace operator as p→1

Behaviour of solutions to p-Laplacian with Robin boundary conditions as p goes to 1

Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators

An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes

An optimal insulation problem

Efficiency and localisation for the first Dirichlet eigenfunction

Saturation phenomena for some classes of nonlinear nonlocal eigenvalue problems

Symmetrization with respect to mixed volumes

A sharp weighted anisotropic Poincaré inequality for convex domains

On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators

A saturation phenomenon for a nonlinear nonlocal eigenvalue problem

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

Some remarks on a shape optimization problem

Sharp estimates and existence for anisotropic elliptic problems with general growth in the gradient

Faber-Krahn inequality for anisotropic eigenvalue problems with Robin boundary conditions

Symmetry breaking in a constrained Cheeger type isoperimetric inequality

Stability results for some fully nonlinear eigenvalue estimates

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

Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials

On a nonlinear Robin problem with an absorption term on the boundary and $L^{1}$ data

On the first Robin eigenvalue of the Finsler $p$ -Laplace operator as $p \to 1$

Behaviour of solutions to $p$ -Laplacian with Robin boundary conditions as $p$ goes to $1$