Giorgio Stefani

activity

20162026

most citedA distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up

77 citations · 285 across the 27 of their papers we have counts for

collaborators

29 papers

math.FA2026

Failure of the Pólya-Szegő inequality for the fractional gradient

Giorgio Stefani

We prove that the Pólya-Szegő inequality for the $L^{p}$ norm of the Riesz fractional $s$ -gradient fails for every $p \in [1, 2)$ and $s \in (0, 1)$ , thus providing a negative answer to a…

math.MG2023★ 1 cited

On the monotonicity of weighted perimeters of convex bodies

Giorgio Saracco, Giorgio Stefani

We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analo…

math.AP2023

Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces

Gianluca Crippa, Marco Inversi, Chiara Saffirio +1

We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove th…

math.FA2023★ 1 cited

On sets with finite distributional fractional perimeter

Giovanni E. Comi, Giorgio Stefani

We continue the study of the fine properties of sets having locally finite distributional fractional perimeter. We refine the characterization of their blow-ups and prove a Leibniz…

math.FA2023★ 2 cited

Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula

Giovanni E. Comi, Giorgio Stefani

Given $α \in (0, 1]$ and $p \in [1, + \infty]$ , we define the space $DM^{α, p} (R^{n})$ of $L^{p}$ vector fields whose $α$ -divergence is a finite Radon measure, extending the…

math.AP2023★ 2 cited

Lagrangian stability for a system of non-local continuity equations under Osgood condition

Marco Inversi, Giorgio Stefani

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak me…

math.AP2023★ 4 cited

Full double Hölder regularity of the pressure in bounded domains

Luigi De Rosa, Mickaël Latocca, Giorgio Stefani

We consider Hölder continuous weak solutions $u \in C^{γ} (Ω)$ , $u \cdot n ∣_{\partial Ω} = 0$ , of the incompressible Euler equations on a bounded and simply connected domain $Ω\subset\mat…

math.DG2023★ 12 cited

Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries

Luca Rizzi, Giorgio Stefani

We prove that, on any sub-Riemannian manifold endowed with a positive smooth measure, the Bakry-Émery inequality for the corresponding sub-Laplacian implies the existence of enough…

math.FA2022★ 3 cited

Non-local $B V$ functions and a denoising model with $L^{1}$ fidelity

Konstantinos Bessas, Giorgio Stefani

We study a general total variation denoising model with weighted $L^{1}$ fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel…

math.MG2022★ 13 cited

The Cheeger problem in abstract measure spaces

Valentina Franceschi, Andrea Pinamonti, Giorgio Saracco +1

We consider non-negative $σ$ -finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and e…

math.FA2022★ 9 cited

Failure of the local chain rule for the fractional variation

Giovanni E. Comi, Giorgio Stefani

We prove that the local version of the chain rule cannot hold for the fractional variation defined in arXiv:1809.08575. In the case $n = 1$ , we prove a stronger result, exhibiting…

math.AP2022★ 5 cited

On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains

Luigi De Rosa, Mickaël Latocca, Giorgio Stefani

We prove that the hydrodynamic pressure $p$ associated to the velocity $u \in C^{θ} (Ω)$ , $θ \in (0, 1)$ , of an inviscid incompressible fluid in a bounded and simply connected domain $Ω\s…

math.AP2022★ 7 cited

Weak-strong uniqueness and vanishing viscosity for incompressible Euler equations in exponential spaces

Luigi De Rosa, Marco Inversi, Giorgio Stefani

In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs…

math.FA2021★ 11 cited

Leibniz rules and Gauss-Green formulas in distributional fractional spaces

Giovanni E. Comi, Giorgio Stefani

We apply the results established in arXiv:2109.15263 to prove some new fractional Leibniz rules involving $B V^{α, p}$ and $S^{α, p}$ functions, following the distributional approach…

math.AP2021★ 5 cited

An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces

Gianluca Crippa, Giorgio Stefani

We revisit Yudovich's well-posedness result for the $2$ -dimensional Euler equations for an inviscid incompressible fluid on either a sufficiently regular (not necessarily bounded)…

math.FA2021★ 12 cited

The fractional variation and the precise representative of $B V^{α, p}$ functions

Giovanni E. Comi, Daniel Spector, Giorgio Stefani

We continue the study of the fractional variation following the distributional approach developed in the previous works arXiv:1809.08575, arXiv:1910.13419 and arXiv:2011.03928. We…

math.AP2021★ 22 cited

Existence and uniqueness theorems for some semi-linear equations on locally finite graphs

Andrea Pinamonti, Giorgio Stefani

We study some semi-linear equations for the $(m, p)$ -Laplacian operator on locally finite weighted graphs. We prove existence of weak solutions for all $m \in N$ and $p\in(1,…

math.MG2021★ 1 cited

On the convex components of a set in $R^{n}$

Flavia Giannetti, Giorgio Stefani

We prove a lower bound on the number of the convex components of a compact set with non-empty interior in $R^{n}$ for all $n \geq 2$ . Our result generalizes and improves the in…

math.AP2021★ 5 cited

On the Steiner property for planar minimizing clusters. The anisotropic case

Valentina Franceschi, Aldo Pratelli, Giorgio Stefani

In this paper we discuss the Steiner property for minimal clusters in the plane with an anisotropic double density. This means that we consider the classical isoperimetric problem…

math.FA2020★ 34 cited

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II

Elia Bruè, Mattia Calzi, Giovanni E. Comi +1

We continue the study of the space $B V^{α} (R^{n})$ of functions with bounded fractional variation in $R^{n}$ and of the distributional fractional Sobolev space $S^{α,p}(\…

math.MG2020★ 2 cited

Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Giorgio Stefani

We study a generalization of the Bakry-Émery pointwise gradient estimate for the heat semigroup and its equivalence with some entropic inequalities along the heat flow and Wasserst…

math.FA2019★ 37 cited

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I

Giovanni E. Comi, G. Stefani

We continue the study of the space $B V^{α} (R^{n})$ of functions with bounded fractional variation in $R^{n}$ of order $α \in (0, 1)$ introduced in arXiv:1809.08575, by dea…

math.FA2018★ 77 cited

A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up

Giovanni E. Comi, Giorgio Stefani

We introduce the new space $B V^{α} (R^{n})$ of functions with bounded fractional variation in $R^{n}$ of order $α \in (0, 1)$ via a new distributional approach exploiting…

math.CA2018★ 5 cited

A maximal function characterization of absolutely continuous measures and Sobolev functions

Elia Bruè, Quoc-Hung Nguyen, Giorgio Stefani

In this note, we give a new characterisation of Sobolev $W^{1, 1}$ functions among $B V$ functions via Hardy-Littlewood maximal function. Exploiting some ideas coming from the proof…

Failure of the Pólya-Szegő inequality for the fractional gradient

On the monotonicity of weighted perimeters of convex bodies

Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces

On sets with finite distributional fractional perimeter

Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula

Lagrangian stability for a system of non-local continuity equations under Osgood condition

Full double Hölder regularity of the pressure in bounded domains

Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries

Non-local BV functions and a denoising model with L1 fidelity

The Cheeger problem in abstract measure spaces

Failure of the local chain rule for the fractional variation

On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains

Weak-strong uniqueness and vanishing viscosity for incompressible Euler equations in exponential spaces

Leibniz rules and Gauss-Green formulas in distributional fractional spaces

An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces

The fractional variation and the precise representative of BVα,p functions

Existence and uniqueness theorems for some semi-linear equations on locally finite graphs

On the convex components of a set in Rn

On the Steiner property for planar minimizing clusters. The anisotropic case

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II

Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I

A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up

A maximal function characterization of absolutely continuous measures and Sobolev functions

Non-local $B V$ functions and a denoising model with $L^{1}$ fidelity

The fractional variation and the precise representative of $B V^{α, p}$ functions

On the convex components of a set in $R^{n}$