Tommaso Bertin

collaborators

3 papers

math.AP2025

Relaxation for highly discontinuous, possibly unbounded, integral functionals

Tommaso Bertin, Giulia Treu

We consider the functional \[ F(u)=\int_Î© f(\nabla u)\,dx\qquad u\inÏ+W^{1,1}_0(Î©) \] where $I^c ◯$ is a Lipschitz bounded open set of $R^{N}$ , $f : R^{N} \to R \cup {+ \infty}$ is a su…

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 $E [f] : u \mapsto \int_{I^} c ◯ f (x, u (x), \nabla u (x)) d x,$ with an emphasis on the non-convex case, and the diff…

math.AP2025

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

Tommaso Bertin

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