$\Gamma$-convergence of free discontinuity problems for circle-valued maps in the linear regime
Analysis of PDEs
2026-01-29 v1
Abstract
We investigate the -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 -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}
}
Comments
24 pages