Abstract

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

Author information

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Baisheng Yan

Dept. of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.

yan@math.msu.edu

Mathematics Subject Classification

49J24, 49J45

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Suggested citation

B. Yan. “On p-Quasiconvex Hulls of Matrix Sets.” Journal of Convex Analysis 14 (2007), No. 4, 879–889. https://doi.org/10.68381/jca14050

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press.