Comptes Rendus
Partial Differential Equations
Lifting of BV functions with values in S1
[Relèvement des fonctions BV à valeurs sur le cercle S1]
Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 159-164.

On montre que pour tout , il existe une fonction à variation bornée telle que u=eiϕ p.p. dans et |ϕ|BV⩽2|u|BV. La constante 2 est optimale en dimension n>1.

We show that for every , there exists a bounded variation function such that u=eiϕ a.e. on and |ϕ|BV⩽2|u|BV. The constant 2 is optimal in dimension n>1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00314-5

Juan Dávila 1 ; Radu Ignat 2

1 Departamento de Ingenierı́a Matemática, CMM (UMR CNRS), Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
2 École normale supérieure, 45, rue d'Ulm, 75230 Paris cedex 05, France
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Juan Dávila; Radu Ignat. Lifting of BV functions with values in S1. Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 159-164. doi : 10.1016/S1631-073X(03)00314-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00314-5/

[1] L. Ambrosio; G. Dal Maso A general chain rule for distributional derivatives, Proc. Amer. Math. Soc., Volume 108 (1990), pp. 691-702

[2] L. Ambrosio; N. Fusco; D. Pallara Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, Oxford, 2000

[3] F. Bethuel; X.M. Zheng Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal., Volume 80 (1988), pp. 60-75

[4] J. Bourgain; H. Brezis; P. Mironescu Lifting in Sobolev spaces, J. Anal. Math., Volume 80 (2000), pp. 37-86

[5] J. Bourgain, H. Brezis, P. Mironescu, H1/2 maps with values into the circle: minimal connections, lifting and the Ginzburg–Landau equation, in press

[6] H. Brezis; L. Nirenberg Degree theory and BMO. I. Compact manifolds without boundaries, Selecta Math. (N.S.), Volume 1 (1995), pp. 197-263

[7] R.R. Coifman; Y. Meyer Une généralisation du théorème de Calderón sur l'intégrale de Cauchy, Fourier Analysis (Proc. Sem., El Escorial, 1979), Asoc. Mat. Española, Madrid, 1980, pp. 87-116

[8] M. Giaquinta; G. Modica; J. Soucek Cartesian Currents in the Calculus of Variations, Vol. II, Springer, 1998

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