The relaxed area of 𝕊1-valued singular maps in the strictBV-convergence

Abstract

Given a bounded open set Ω ⊂ ℝ2, we study the relaxation of the nonparametric area functional in the strict topology inBV(Ω; ℝ2). and compute it for vortex-type maps, and more generally for maps inW1,1(Ω;S1) having a finite number of topological singularities. We also extend the analysis to some specific piecewise constant maps inBV(Ω;S1), including the symmetric triple junction map.