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On rank-one convex and polyconvex conformal energy functions with slow growth

Published online by Cambridge University Press:  14 November 2011

Baisheng Yan
Baisheng Yan
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A., e-mail: yan@math.msu.edu
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Abstract

We make some remarks about rank-one convex and polyconvex functions on the set of all real n × n matrices that vanish on the subset Kn consisting of all conformal matrices and grow like a power function at infinity. We prove that every non-negative rank-one convex function that vanishes on Kn and grows below a power of degree n/2 must vanish identically. In odd dimensions n ≧ 3, we prove that every non-negative polyconvex function that vanishes on Kn must vanish identically if it grows below a power of degree n; while in even dimensions, such polyconvex functions can exist that also grow like a power of half-dimension degree.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 3 , 1997 , pp. 651 - 663
Copyright
Copyright © Royal Society of Edinburgh 1997

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