| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 56 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2022049 | |
| Published online | 18 August 2022 | |
The relaxed area of 𝕊1-valued singular maps in the strict BV-convergence*
1 Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Universita di Siena, 53100 Siena, Italy
2 International Centre for Theoretical Physics ICTP, Mathematics Section, 34151 Trieste, Italy
3 Area of Mathematical Analysis, Modelling, and Applications, Scuola Internazionale Superiore di Studi Avanzati “SISSA”, Via Bonomea, 265, 34136 Trieste, Italy
** Corresponding author: riccardo.scala@unisi.it
Received:
10
February
2022
Accepted:
4
July
2022
Given a bounded open set Ω ⊂ ℝ2, we study the relaxation of the nonparametric area functional in the strict topology in BV(Ω; ℝ2). and compute it for vortex-type maps, and more generally for maps in W1,1(Ω;S1) having a finite number of topological singularities. We also extend the analysis to some specific piecewise constant maps in BV(Ω;S1), including the symmetric triple junction map.
Mathematics Subject Classification: 49J45 / 49Q05 / 49Q15 / 28A75
Key words: Area functional / relaxation / Cartesian currents / total variation of the Jacobian / S1-valued singular maps
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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