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.
The relaxed area of S1-valued singular maps in the strict BV-convergence
Giovanni Bellettini;
2022-01-01
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.File in questo prodotto:
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