Geodesic
On L1-Lower Semicontinuity in BV
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 173-185.

Voir la notice de l'article provenant de la source Heldermann Verlag

A new lower semicontinuity theorem for integral functionals defined on the space BV of functions of bounded variation is proved. This result is obtained by replacing the continuity of the energy density f with respect to the space variable x with a weak differentiability assumption. The proof is based on a new integration by parts formula in the space BV which does not seem to be contained in any of the similar results known in the literature and which could be of independent interest. 
@article{JCA_2005_12_1_JCA_2005_12_1_a11,
     author = {V. De Cicco and N. Fusco and A. Verde},
     title = {On {L\protect\textsuperscript{1}-Lower} {Semicontinuity} in {BV}},
     journal = {Journal of convex analysis},
     pages = {173--185},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2005},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a11/}
}
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V. De Cicco; N. Fusco; A. Verde. On L1-Lower Semicontinuity in BV. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 173-185. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a11/