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.
Bellettini, G., Carano, S., Scala, R. (2022). The relaxed area of S1-valued singular maps in the strict BV-convergence. ESAIM. COCV, 28 [10.1051/cocv/2022049].
The relaxed area of S1-valued singular maps in the strict BV-convergence
Giovanni Bellettini;Riccardo Scala
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.
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https://hdl.handle.net/11365/1213714