Rank-one convexity implies quasi-convexity on certain hypersurfaces

Author： Chaudhuri Nirmalendu   Müller Stefan  

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.133, Iss.6, 2003-12, pp. : 1263-1272

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Abstract

We show that, if f : M2×2 → R is rank-one convex on the hyperboloid H-D := {X ∈ S2×2 : det X = -D, X11 ≥ 0}, D ≥ 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.

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