Rigidity for the four gradient problem

Miroslav Chlebík and Bernd Kirchheim

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Submission date: 18. May. 2000
Pages: 9
published in: Journal für die reine und angewandte Mathematik, 551 (2002), p. 1-9 
DOI number (of the published article): 10.1515/crll.2002.082, 30/09/2002
Bibtex
MSC-Numbers: 49K24
Keywords and phrases: rigidity, rank-one connection, gradients, bounded distortion
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Abstract:
We prove a general rigidity result for the maximal possible number of gradients by showing that any lipschitz function using four pairwise not rank-one connected gradients is necessarily affine. This exhibits an interesting difference between rigidity features of approximate and exact solutions of differential inclusions.