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.
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.
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Micol Amar 1; Virginia De Cicco 1
@article{CRMATH_2005__340_10_735_0,
author = {Micol Amar and Virginia De Cicco},
title = {A new approximation result for {BV-functions}},
journal = {Comptes Rendus. Math\'ematique},
pages = {735--738},
year = {2005},
publisher = {Elsevier},
volume = {340},
number = {10},
doi = {10.1016/j.crma.2005.03.027},
language = {en},
}
Micol Amar; Virginia De Cicco. A new approximation result for BV-functions. Comptes Rendus. Mathématique, Volume 340 (2005) no. 10, pp. 735-738. doi: 10.1016/j.crma.2005.03.027
[1] 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] Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, New York, 2000
[3] Strong approximation of GSBV functions by piecewise smooth functions, Ann. Univ. Ferrara Sez. VII (N.S.), Volume 43 (1998), pp. 27-49
[4] A density result in SBV with respect to non-isotropic energies, Nonlinear Anal., Volume 38 (1999), pp. 585-604
[5] An approximation result for the minimizers of the Mumford–Shah functional, Boll. Un. Mat. Ital., Volume 11-A (1997), pp. 149-162
[6] Geometric Measure Theory, Springer-Verlag, Berlin, 1969
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