On jump minimizing liftings for ${\mathbb{S}}^1$-valued maps and connections with Ambrosio-Tortorelli-type $\Gamma$-limits

Giovanni Bellettini, Roberta Marziani, Riccardo Scala

This paper is concerned with the $\Gamma$-limits of Ambrosio-Tortorelli-type functionals, for maps $u$ defined on an open bounded set $\Omega \subset {\mathbb{R}}^n$ and taking values in the unit…