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 / Bellettini, G.; Carano, S.; Scala, R.. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 28:(2022), pp. 1-38. [10.1051/cocv/2022049]
The relaxed area of S1-valued singular maps in the strict BV-convergence
Bellettini, G.;Carano, S.;Scala, R.
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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Descrizione: We compute the relaxed Cartesian area in the strict $BV$-convergence on a class of piecewise Lipschitz maps from the plane to the plane, having jump made of several curves allowed to meet at a finite number of junction points. We show that the domain of this relaxed area is strictly contained in the domain of the classical $L^1$-relaxed area.
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