Functional Analysis
A new approximation result for BV-functions
[Un nouveau résultat d'approximation pour fonctions BV]
Comptes Rendus. Mathématique, Tome 340 (2005) no. 10, pp. 735-738.

On démontre un théorème de approximation pour une fonction qui appartient à l'espace BV avec une suite quasi-polyédriques de fonctions BV. Cette approximation peut être très utile pour quelques problèmes du Calcul des Variations.

This Note is devoted to obtaining an approximation result for BV-functions by means of a quasi-polyhedral sequence of BV-functions. This approximation could have interesting applications in some problems of the Calculus of Variations.

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Accepté le :
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DOI : 10.1016/j.crma.2005.03.027
Amar, Micol 1 ; De Cicco, Virginia 1

1 Università di Roma “La Sapienza”, Dipartimento di Metodi e Modelli Matematici, Via A. Scarpa 16, 00161 Roma, Italy
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Amar, Micol; De Cicco, Virginia. A new approximation result for BV-functions. Comptes Rendus. Mathématique, Tome 340 (2005) no. 10, pp. 735-738. doi : 10.1016/j.crma.2005.03.027. http://archive.numdam.org/articles/10.1016/j.crma.2005.03.027/

[1] Ambrosio, L.; Fusco, N.; Hutchinson, J.E. Higher integrability of the gradient and dimension of the singular set for minimizers of the Mumford–Shah functional, Calc. Var. Partial Differential Equations (2), Volume 16 (2003), pp. 187-215

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

[3] Cortesani, G. Strong approximation of GSBV functions by piecewise smooth functions, Ann. Univ. Ferrara Sez. VII (N.S.), Volume 43 (1998), pp. 27-49

[4] Cortesani, G.; Toader, R. A density result in SBV with respect to non-isotropic energies, Nonlinear Anal., Volume 38 (1999), pp. 585-604

[5] Dibos, F.; Séré, E. An approximation result for the minimizers of the Mumford–Shah functional, Boll. Un. Mat. Ital., Volume 11-A (1997), pp. 149-162

[6] Federer, H. Geometric Measure Theory, Springer-Verlag, Berlin, 1969

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