Volume 28, 2022
|Number of page(s)||38|
|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: firstname.lastname@example.org
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.