F. Prinari

activity

20062026

most citedOn the radiality of constrained minimizers to the Schroedinger-Poisson-Slater energy

34 citations · 36 across the 17 of their papers we have counts for

collaborators

19 papers

math.AP2026

Sharp Makai-type inequalities for the best Poincaré-Sobolev constants

Giovanni Pisante, Francesca Prinari

Given a bounded convex open set $Ω \subseteq R^{N}$ , we prove that the Poincaré-Sobolev constants $λ_{p, q} (Ω)$ can be bounded from below by the $p$ -power of the ratio between…

math.OC2026

Stochastic homogenization of nonconvex unbounded integral functionals with generalized Orlicz growth

Davide Aruta, Francesca Prinari, Francesco Solombrino

We consider the homogenization of random integral functionals which are possibly unbounded, that is, the domain of the integrand is not the whole space and may depend on the space-…

math.AP2026

Low eigenvalues of the $p -$ Laplacian in general open sets

Lorenzo Brasco, Luca Briani, Francesca Prinari

We consider the minmax Ljusternik-Schnirelmann levels of the constrained $p -$ Dirichlet integral, on a general open set of the Euclidean space. We show that, whenever one of these l…

math.AP2025

Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond

Lorenzo Brasco, Luca Briani, Francesca Prinari

We consider periodically perforated unbounded open sets and prove existence of extremals for the relevant sharp Poincaré-Sobolev embedding constant. The existence result holds no m…

math.AP2025

Extremals for Poincaré-Sobolev sharp constants in Steiner symmetric sets

Lorenzo Brasco, Luca Briani, Francesca Prinari

We prove existence of minimizers for the sharp Poincaré-Sobolev constant in general Steiner symmetric sets, in the subcritical and superhomogeneous regime. The sets considered are…

math.AP2024

On fractional Hardy-type inequalities in general open sets

Eleonora Cinti, Francesca Prinari

We show that, when $s p > N$ , the sharp Hardy constant $h_{s, p}$ of the punctured space $R^{N} ∖ {0}$ in the Sobolev-Slobodecki\uı space provides an optimal l…

math.AP2023

On Morrey's inequality in Sobolev-Slobodecki\uı spaces

Lorenzo Brasco, Francesca Prinari, Firoj Sk

We study the sharp constant in the Morrey inequality for fractional Sobolev-Slobodecki\uı spaces on the whole $R^{N}$ . By generalizing a recent work by Hynd and Seuffert, we…

math.OC2023

On the sharp Makai inequality

Francesca Prinari, Anna Chiara Zagati

On a convex bounded open set, we prove that Poincaré-Sobolev constants for functions vanishing at the boundary can be bounded from below in terms of the norm of the distance functi…

math.AP2023

Asymptotic analysis of thin structures with point dependent energy growth

Michela Eleuteri, Francesca Prinari, Elvira Zappale

$3 d - 2 d$ dimensional reduction for hyperelastic thin films modeled through energies with point dependent growth, assuming that the sample is clamped on the lateral boundary, is perf…

math.AP2023

Sobolev embeddings and distance functions

Lorenzo Brasco, Francesca Prinari, Anna Chiara Zagati

On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $D_{0}^{1, p}$ into $L^{q}$ and the summability prop…

math.OC2021

On a class of Cheeger inequalities

Luca Briani, Giuseppe Buttazzo, Francesca Prinari

We study a general version of the Cheeger inequality by considering the shape functional $F_{p, q} (Ω) = λ_{p}^{1/ p} (Ω) / λ_{q} (Ω)^{1/ q}$ . The infimum and the supremum of $\mathcal…

math.AP2021

A comparison principle for the Lane-Emden equation and applications to geometric estimates

Lorenzo Brasco, Francesca Prinari, Anna Chiara Zagati

We prove a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the $p -$ Laplacian, with subhomogeneous power in the right-hand side. The…

math.OC2021★ 1 cited

A shape optimization problem on planar sets with prescribed topology

L. Briani, G. Buttazzo, F. Prinari

We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(…

math.AP2020★ 1 cited

Some inequalities involving perimeter and torsional rigidity

L. Briani, G. Buttazzo, F. Prinari

We consider shape functionals of the form $F_{q} (Ω) = P (Ω) T^{q} (Ω)$ on the class of open sets of prescribed Lebesgue measure. Here $q > 0$ is fixed, $P (Ω)$ denotes the perimeter of $Ω$ and…

math.OC2020

$Γ$ -convergence for power-law functionals with variable exponents

Francesca Prinari, Michela Eleuteri

We study the $Γ$ -convergence of the functionals $F_{n} (u) := ∣∣ f (\cdot, u (\cdot), D u (\cdot)) ∣ ∣_{p_{n} (\cdot)}$ and $F_{n} (u) := \int_{Ω} \frac{1}{p _{n} ( x )} f^{p_{n} (x)} (x, u (x), D u (x)) d x$ …

math.OC2019

A relaxation result in the vectorial setting and $L^{p}$ -approximation for $L^{\infty}$ -functionals

Francesca Prinari, Elvira Zappale

We provide relaxation for not lower semicontinuous supremal functionals of the type $W^{1,\infty}(Ω;\mathbb R^d) \ni u \mapsto\supess_{ x \in Ω}f(\nabla u(x))$ in the vectorial cas…

math.OC2018

The role of intrinsic distances in the relaxation of $L^{\infty}$ -functionals

Maria Stella Gelli, Francesca Prinari

We consider a supremal functional of the form $F (u) = ess sup_{x \in Ω} f (x, D u (x))$ where $Ω \subseteq R^{N}$ is a regular bounded open set, $u\in W^{1,\inft…

math.AP2011★ 34 cited

On the radiality of constrained minimizers to the Schroedinger-Poisson-Slater energy

Vladimir Georgiev, Francesca Prinari, Nicola Visciglia

We study the radial symmetry of minimizers to the Schroedinger-Poisson-Slater (S-P-S) energy.

math.AP2006

On the Yamabe equation with rough potentials

Francesca Prinari, Nicola Visciglia

We study the existence of non--trivial solutions to the Yamabe equation: $- Δ u + a (x) = μu ∣ u ∣^{\frac{4}{n - 2}} μ > 0, x \in Ω \subset R^{n} with n \geq 4,$ $$ u(x)=0 \h…

Sharp Makai-type inequalities for the best Poincaré-Sobolev constants

Stochastic homogenization of nonconvex unbounded integral functionals with generalized Orlicz growth

Low eigenvalues of the p−Laplacian in general open sets

Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond

Extremals for Poincaré-Sobolev sharp constants in Steiner symmetric sets

On fractional Hardy-type inequalities in general open sets

On Morrey's inequality in Sobolev-Slobodecki\uı spaces

On the sharp Makai inequality

Asymptotic analysis of thin structures with point dependent energy growth

Sobolev embeddings and distance functions

On a class of Cheeger inequalities

A comparison principle for the Lane-Emden equation and applications to geometric estimates

A shape optimization problem on planar sets with prescribed topology

Some inequalities involving perimeter and torsional rigidity

Γ-convergence for power-law functionals with variable exponents

A relaxation result in the vectorial setting and Lp-approximation for L∞-functionals

The role of intrinsic distances in the relaxation of L∞-functionals

On the radiality of constrained minimizers to the Schroedinger-Poisson-Slater energy

On the Yamabe equation with rough potentials

Low eigenvalues of the $p -$ Laplacian in general open sets

$Γ$ -convergence for power-law functionals with variable exponents

A relaxation result in the vectorial setting and $L^{p}$ -approximation for $L^{\infty}$ -functionals

The role of intrinsic distances in the relaxation of $L^{\infty}$ -functionals