Some examples of rank one convex functions in dimension two-Reference-Cited by-同舟云学术

Some examples of rank one convex functions in dimension two

Published:1990 Issue:1-2 Volume:114 Page:135-150
ISSN:0308-2105
Container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics
language:en
Short-container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Author:

Dacorogna B.,Douchet J.,Gangbo W.,Rappaz J.

Abstract

SynopsisWe study the rank one convexity of some functionsf(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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference20 articles.

1. Sur l'extension de la condition de Legendre du calcul des variations aux intégrales multiples à plusieurs fonctions inconnues;Hove;Proc. Koninkl. Ned. Akad.,1947

2. Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung

3. A theorem on quadratic forms

4. Multiple Integrals in the Calculus of Variations

5. Quasiconvex quadratic forms in two dimensions

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