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

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5 papers · 1 filter

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.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…