Rank-one convexity implies quasi-convexity on certain hypersurfaces

Authors: Chaudhuri N.; Müller S.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 133, Number 6, 19 December 2003 , pp. 1263-1272(10)

Publisher: Royal Society of Edinburgh

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Abstract:

We show that, if f : M2×2 rarr R is rank-one convex on the hyperboloid H-D := {X isin S2×2 : det X = -D, X11 ge 0}, D ge 0, S2×2 is the set of 2×2 real symmetric matrices, then f can be approximated by quasi-convex functions on M2×2 uniformly on compact subsets of H-D. Equivalently, every gradient Young measure supported on a compact subset of H-D is a laminate.

Document Type: Research article

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