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

Giovanni Bellettini; Roberta Marziani; Riccardo Scala

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arXiv · 2601.20612

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

Giovanni Bellettini·Roberta Marziani·Riccardo Scala

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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.

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Giovanni Bellettini, Roberta Marziani, Riccardo Scala. 2026-01-28. $\Gamma$-convergence of free discontinuity problems for circle-valued maps in the linear regime. https://arxiv.org/abs/2601.20612

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