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Some examples of rank one convex functions in dimension two

Published online by Cambridge University Press:  14 November 2011

B. Dacorogna ,
J. Douchet ,
W. Gangbo  and
J. Rappaz
B. Dacorogna
Affiliation:
Département de Mathématiques, E.P.F.L., 1015 Lausanne, Switzerland
J. Douchet
Affiliation:
Département de Mathématiques, E.P.F.L., 1015 Lausanne, Switzerland
W. Gangbo
Affiliation:
Département de Mathématiques, E.P.F.L., 1015 Lausanne, Switzerland
J. Rappaz
Affiliation:
Département de Mathématiques, E.P.F.L., 1015 Lausanne, Switzerland
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Synopsis

We study the rank one convexity of some functions f(ξ) where ξ is a 2 × 2 matrix. Examples such as |ξ|2α + h(detξ) and | ξ |2α (| ξ |2 − γdet ξ) are investigated. Numerical computations are done on the example of Dacorogna and Marcellini, indicating that this function is quasiconvex.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 135 - 150
Copyright
Copyright © Royal Society of Edinburgh 1990

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