ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Abstract
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.
