Calculus of Variations and Geometric Measure Theory

G. Bellettini - R. Marziani - R. Scala

$\Gamma$-convergence of free discontinuity problems for circle-valued maps in the linear regime

created by marziani on 28 Jan 2026

[BibTeX]

Preprint

Inserted: 28 jan 2026
Last Updated: 28 jan 2026

Year: 2026

Abstract:

We investigate the $\Gamma$-convergence of Ambrosio–Tortorelli type-functionals for circle valued functions, in the case of volume terms with linear growth. We show the emergence of a non-local $\Gamma$-limit, which is due to the topological structure of the target space, and discuss compactness of minimal liftings. Our results extend the analysis of a previous work on the quadratic case.

Keywords: Minimizing liftings, $\Gamma$-convergence, Circle-valued maps


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