Geodesic
Quasi Convex Integrands and Lower Semicontinuity in BV
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 369-386 
P. Brandi; A. Salvadori. Quasi Convex Integrands and Lower Semicontinuity in BV. Journal of convex analysis, Tome 8 (2001) no. 2, pp. 369-386. http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a3/
@article{JCA_2001_8_2_JCA_2001_8_2_a3,
     author = {P. Brandi and A. Salvadori},
     title = {Quasi {Convex} {Integrands} and {Lower} {Semicontinuity} in {BV}},
     journal = {Journal of convex analysis},
     pages = {369--386},
     year = {2001},
     volume = {8},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a3/}
}
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%J Journal of convex analysis
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Voir la notice de l'article provenant de la source Heldermann Verlag

We discuss the lower semicontinuity of multiple integrals of the calculus of variations, for quasi convex integrands in BV setting. The main result is a lower semicontinuity theorem with respect to weak convergence in BV, i.e. L1-convergence of equi-BV sequences, under mild assumptions on the integrand. The approach we propose here is based on two main results: