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arXiv · 2305.10584

The relaxed area of $\mathcal{S}^1$-valued singular maps in the strict $BV$-convergence

Giovanni Bellettini·Simone Carano·Riccardo Scala
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Abstract

Given a bounded open set $Ω\subset \mathbb{R}^2$, we study the relaxation of the nonparametric area functional in the strict topology in $BV(Ω;\mathbb{R}^2)$, and compute it for vortex-type maps, and more generally for maps in $W^{1,1}(Ω;\mathcal{S}^1)$ having a finite number of topological singularities. We also extend the analysis to some specific piecewise constant maps in $BV(Ω;\mathcal{S}^1)$, including the symmetric triple junction map.

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Giovanni Bellettini, Simone Carano, Riccardo Scala. 2023-05-17. The relaxed area of $\mathcal{S}^1$-valued singular maps in the strict $BV$-convergence. https://arxiv.org/abs/2305.10584

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