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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@article{CRMATH_2005__340_10_735_0, author = {Amar, Micol and De Cicco, Virginia}, title = {A new approximation result for {BV-functions}}, journal = {Comptes Rendus. Math\'ematique}, pages = {735--738}, publisher = {Elsevier}, volume = {340}, number = {10}, year = {2005}, doi = {10.1016/j.crma.2005.03.027}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.03.027/} }
TY - JOUR AU - Amar, Micol AU - De Cicco, Virginia TI - A new approximation result for BV-functions JO - Comptes Rendus. Mathématique PY - 2005 SP - 735 EP - 738 VL - 340 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.03.027/ DO - 10.1016/j.crma.2005.03.027 LA - en ID - CRMATH_2005__340_10_735_0 ER -
%0 Journal Article %A Amar, Micol %A De Cicco, Virginia %T A new approximation result for BV-functions %J Comptes Rendus. Mathématique %D 2005 %P 735-738 %V 340 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.03.027/ %R 10.1016/j.crma.2005.03.027 %G en %F CRMATH_2005__340_10_735_0
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] 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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