$Γ$-convergence of free discontinuity problems for circle-valued maps in the linear regime
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917227617320960 |
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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 |