Preprint 18/1997

A sharp version of Zhang's theorem on truncating sequences of gradients

Stefan Müller

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Submission date: 31. Jul. 1997
Pages: 22
published in: Transactions of the American Mathematical Society, 351 (1999) 11, p. 4585-4597 
MSC-Numbers: 49J45
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Abstract:
Let img25 be a compact and convex set of img27 matrices and let img29 be a sequence in 31 that converges to K in the mean, i.e. img35. I show that there exists a sequence 37 of Lipschitz functions such that img39 and img41. This refines a result of Kewei Zhang (Ann. S.N.S. Pisa 19 (1992), 313-326) who showed that one may assume img43. Applications to gradient Young measures and to a question of Kinderlehrer and Pedregal (Arch. Rat. Mech. Anal. 115 (1991), 329-365) regarding the approximation of img45 valued quasiconvex functions by finite ones are indicated. A challenging open problem is whether convexity of K can be replaced by quasiconvexity.

21.02.2013, 01:40