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On non-negative quasiconvex functions with unbounded zero sets

Published online by Cambridge University Press:  14 November 2011

Kewei Zhang
Kewei Zhang
Affiliation:
School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney NSW 2109, Australia E-mail: kewei@macadam.mpce.mq.edu.au
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Abstract

We construct nontrivial, non-negative quasiconvex functions denned on M2×2 with p-th order growth such that the zero sets of the functions are Lipschitz graphs of mappings from subsets of a fixed two-dimensional subspace to its orthogonal complement. We assume that the graphs do not have rank-one connections with the Lipschitz constants sufficiently small. In particular, we are able to construct quasiconvex functions which are homogeneous of degree p (p > 1) and ‘conjugating’ invariant.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 411 - 422
Copyright
Copyright © Royal Society of Edinburgh 1997

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