Federico Franceschini

activity

20142026

most citedFree boundary partial regularity in the thin obstacle problem

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

collaborators

9 papers

math.AP2026

Mean curvature bounds for the obstacle problem

Giacomo Colombo, Federico Franceschini

We prove optimal $(n - 1)$ -semiconvexity estimates for solutions to the classical obstacle problem, possibly with a smooth right-hand side. We deduce that the mean curvature of the f…

math.AP2026

Stable Semilinear Elliptic Equations: $ε$ -Regularity à la Brezis and Dimensional Bounds for the Singular Set

Alessio Figalli, Federico Franceschini

We develop a quantitative partial regularity theory for stable solutions of \[ -Δu=f(u), \] where $f : R \to [0, + \infty]$ is increasing and convex. The theory is uniform in t…

math.DG2026

Minimal Surfaces with Stratified Branching Sets

Federico Franceschini, Rafe Mazzeo, Paul Minter

Inspired by the Taubes-Wu construction of $C^{1, α}$ two-valued harmonic functions by the use of symmetry, we construct minimal surfaces with stratified branching sets as…

math.AP2021★ 4 cited

Free boundary partial regularity in the thin obstacle problem

Federico Franceschini, Joaquim Serra

For the thin obstacle problem in $R^{n}$ , $n \geq 2$ , we prove that at all free boundary points, with the exception of a $(n - 3)$ -dimensional set, the solution differs from it…

math.AP2021

Expansion of the fundamental solution of a second-order elliptic operator with analytic coefficients

Federico Franceschini, Federico Glaudo

Let $L$ be a second-order elliptic operator with analytic coefficients defined in $B_{1} \subseteq R^{n}$ . We construct explicitly and canonically a fundamental solution for the…

math.AP2021★ 3 cited

$C^{\infty}$ partial regularity of the singular set in the obstacle problem

Federico Franceschini, Wiktoria Zatoń

We show that the singular set $Σ$ in the classical obstacle problem can be locally covered by a $C^{\infty}$ hypersurface, up to an "exceptional" set $E$ , which has Hausdorff dimensi…

math.GR2017

The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups

Federico Franceschini, Roberto Frigerio, Maria Beatrice Pozzetti +1

We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a ne…

math.GR2015

A characterization of relatively hyperbolic groups via bounded cohomology

Federico Franceschini

It was proved by Mineyev and Yaman that, if $(Γ, Γ^{'})$ is a relatively hyperbolic pair, the comparison map $H_{b}^{k} (Γ, Γ^{'}; V) \to H^{k} (Γ, Γ^{'}; V)$ is surjective for every $k \geq 2$ ,…

math.GT2014★ 1 cited

Proportionality Principle for the Lipschitz simplicial volume

Federico Franceschini

We prove the Proportionality Principle for the Lipschitz simplicial volume without any restriction on curvature. Our argument is based on the construction of a suitable \emph{pseud…

Mean curvature bounds for the obstacle problem

Stable Semilinear Elliptic Equations: ε-Regularity à la Brezis and Dimensional Bounds for the Singular Set

Minimal Surfaces with Stratified Branching Sets

Free boundary partial regularity in the thin obstacle problem

Expansion of the fundamental solution of a second-order elliptic operator with analytic coefficients

C∞ partial regularity of the singular set in the obstacle problem

The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups

A characterization of relatively hyperbolic groups via bounded cohomology

Proportionality Principle for the Lipschitz simplicial volume

Stable Semilinear Elliptic Equations: $ε$ -Regularity à la Brezis and Dimensional Bounds for the Singular Set

$C^{\infty}$ partial regularity of the singular set in the obstacle problem