English

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

Analysis of PDEs 2026-01-29 v1

Abstract

We investigate the Γ\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 Γ\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

Cite

@article{arxiv.2601.20612,
  title  = {$\Gamma$-convergence of free discontinuity problems for circle-valued maps in the linear regime},
  author = {Giovanni Bellettini and Roberta Marziani and Riccardo Scala},
  journal= {arXiv preprint arXiv:2601.20612},
  year   = {2026}
}

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24 pages