Partial Differential Equations
Lifting of BV functions with values in S1
[Relèvement des fonctions BV à valeurs sur le cercle S1]

Présenté par : Haïm Brezis

Dávila, Juan1 ; Ignat, Radu2
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
Comptes Rendus. Mathématique, Tome 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
Dávila, Juan 1 ; Ignat, Radu 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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     title = {Lifting of {BV} functions with values in {\protect\emph{S}\protect\textsuperscript{1}}},
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Dávila, Juan; Ignat, Radu. Lifting of BV functions with values in S1. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 159-164. doi : 10.1016/S1631-073X(03)00314-5. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00314-5/

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

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

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

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

[7] Coifman, R.R.; Meyer, Y. 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] Giaquinta, M.; Modica, G.; Soucek, J. Cartesian Currents in the Calculus of Variations, Vol. II, Springer, 1998

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