Journal of Convex Analysis 14 (2007), No. 4, 879--889
Copyright Heldermann Verlag 2007
On p-Quasiconvex Hulls of Matrix Sets
Dept. of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.
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.
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