Tommaso Bertin

collaborators

3 papers

math.AP2025

Relaxation for highly discontinuous, possibly unbounded, integral functionals

Tommaso Bertin, Giulia Treu

We consider the functional \[ F(u)=\int_Ω f(\nabla u)\,dx\qquad u\inφ+W^{1,1}_0(Ω) \] where $Ω$ is a Lipschitz bounded open set of $R^{N}$ , $f : R^{N} \to R \cup {+ \infty}$ is a superl…

math.AP2025

Relaxation of Non-Convex Integral Functionals in the Multidimensional Scalar Case

Tommaso Bertin, Paulin Huguet

We study integral functionals defined on scalar Sobolev spaces of the form $E [f] : u \mapsto \int_{Ω} f (x, u (x), \nabla u (x)) d x,$ with an emphasis on the non-convex case, and the diffi…

math.AP2025

Integral representations of lower semicontinuous envelopes and Lavrentiev Phenomenon for non continuous Lagrangians

Tommaso Bertin

We consider the functional $F_{\infty} (u) = \int_{Ω} f (x, u (x), \nabla u (x)) d x u \in φ + W_{0}^{1, \infty} (Ω, R)$ where $Ω$ is an open bounded Lipschitz subset of $\mathbb{…