Geodesic
On p-Quasiconvex Hulls of Matrix Sets
Journal of convex analysis, Tome 14 (2007) no. 4, pp. 879-889 
B. Yan. On p-Quasiconvex Hulls of Matrix Sets. Journal of convex analysis, Tome 14 (2007) no. 4, pp. 879-889. http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a10/
@article{JCA_2007_14_4_JCA_2007_14_4_a10,
     author = {B. Yan},
     title = {On {p-Quasiconvex} {Hulls} of {Matrix} {Sets}},
     journal = {Journal of convex analysis},
     pages = {879--889},
     year = {2007},
     volume = {14},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a10/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

We present some basic properties and equivalent definitions of the p-quasiconvex hull of a given set of matrices. In particular, we completely characterize the p-quasiconvex hull in terms of the W1,p-gradient Young measures studied by D. Kinderlehrer and P. Pedregal ["Gradient Young measures generated by sequences in Sobolev spaces", J. Geom. Anal. 4 (1994) 59--90] and establish an important relationship with the weak convergence in Sobolev spaces. We also give some simple characterization of the p-quasiconvex hulls for certain special sets.