Riccardo Scala

collaborators

5 papers

math.AP2024

Approximation of topological singularities through free discontinuity functionals: the critical and super-critical regimes

Vito Crismale, Lucia De Luca, Riccardo Scala

We further investigate the properties of an approach to topological singularities through free discontinuity functionals of Mumford-Shah type proposed in \cite{DLSVG}. We prove the…

math.AP2024

On the singular planar Plateau problem

Marco Caroccia, Riccardo Scala

Given any $Γ = γ (S^{1}) \subset R^{2}$ , image of a Lipschitz curve $γ : S^{1} \to R^{2}$ , not necessarily injective, we provide an explicit formula for…

math.AP2023

Upper bounds for the relaxed area of $S^{1}$ -valued Sobolev maps and its countably subadditive interior envelope

Giovanni Bellettini, Riccardo Scala, Giuseppe Scianna

Given a bounded open connected Lipschitz set $Ω \subset R^{2}$ , we show that the relaxed Cartesian area functional $A (u, Ω)$ of a map $u\in W^{1,1}(Ω;\mathb…

math.CA2023

Relaxed area of graphs of piecewise Lipschitz maps in the strict $B V$ -convergence

Giovanni Bellettini, Simone Carano, Riccardo Scala

We compute the relaxed Cartesian area in the strict $B V$ -convergence on a class of piecewise Lipschitz maps from the plane to the plane, having jump made of several curves allowed…

math.CA2023

The relaxed area of $S^{1}$ -valued singular maps in the strict $B V$ -convergence

Giovanni Bellettini, Simone Carano, Riccardo Scala

Given a bounded open set $Ω \subset R^{2}$ , we study the relaxation of the nonparametric area functional in the strict topology in $B V (Ω; R^{2})$ , and compute it for vo…

Approximation of topological singularities through free discontinuity functionals: the critical and super-critical regimes

On the singular planar Plateau problem

Upper bounds for the relaxed area of S1-valued Sobolev maps and its countably subadditive interior envelope

Relaxed area of graphs of piecewise Lipschitz maps in the strict BV-convergence

The relaxed area of S1-valued singular maps in the strict BV-convergence

Upper bounds for the relaxed area of $S^{1}$ -valued Sobolev maps and its countably subadditive interior envelope

Relaxed area of graphs of piecewise Lipschitz maps in the strict $B V$ -convergence

The relaxed area of $S^{1}$ -valued singular maps in the strict $B V$ -convergence