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

Fuente: arXiv
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Main Authors: Bellettini, Giovanni, Marziani, Roberta, Scala, Riccardo
Format: Preprint
Published: 2026
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author Bellettini, Giovanni
Marziani, Roberta
Scala, Riccardo
author_facet Bellettini, Giovanni
Marziani, Roberta
Scala, Riccardo
contents We investigate the $Γ$-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 $Γ$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_20612
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle $Γ$-convergence of free discontinuity problems for circle-valued maps in the linear regime
Bellettini, Giovanni
Marziani, Roberta
Scala, Riccardo
Analysis of PDEs
We investigate the $Γ$-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 $Γ$-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.
title $Γ$-convergence of free discontinuity problems for circle-valued maps in the linear regime
topic Analysis of PDEs
url https://arxiv.org/abs/2601.20612