Some examples of rank one convex functions in dimension two
Dacorogna, B. ; Douchet, J. ; Gangbo, W. ; Rappaz, J.
In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1990, vol. 114, no. 1-2, p. 135-150
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- 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