Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T09:38:08.115Z Has data issue: false hasContentIssue false
  • English
  • Français

On the different convex hulls of sets involving singular values

Published online by Cambridge University Press:  14 November 2011

B. Dacorogna  and
C. Tanteri
B. Dacorogna
Affiliation:
Département de Mathématiques, Ecole Polytechnique Fédérate de Lausanne, CH 1015 Lausanne, Suisse e-mail: [email protected]
C. Tanteri
Affiliation:
Département de Mathématiques, Ecole Polytechnique Fédérate de Lausanne, CH 1015 Lausanne, Suisse e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

We give a representation formula for the convex, polyconvex and rank one convex hulls of a set of n × n matrices with prescribed singular values.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1261 - 1280
Copyright
Copyright © Royal Society of Edinburgh 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Aubert, G. and Tahraoui, R.. Sur la faible fermeture de certains ensembles de contraintes en élasticité non linéaire plan. C. R. Acad. Sci. Paris 290 (1980), 537–40.Google Scholar
2Ball, J. M.. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal 63(1977), 337–403.CrossRefGoogle Scholar
3Dacorogna, B.. Direct Methods in the Calculus of Variations. Applied Mathematical Sciences 78 (New York: Springer, 1989).CrossRefGoogle Scholar
4Dacorogna, B. and Marcellini, P.. Théorème d'existence dans le cas scalaire et vectoriel pour les équations de Hamilton–Jacobi. C. R. Acad. Sci. Paris. Sir. I 322 (1996), 237–40.Google Scholar
5Dacorogna, B. and Marcellini, P.. Sur le probleme de Cauchy–Dirichlet pour les systemes d'equations non linéaires du premier ordre. C. R. Acad. Sci. Paris Sér. I 323 (1996), 599–602.Google Scholar
6Dacorogna, B. and Marcellini, P.. General existence theorems for Hamilton–Jacobi equations in the scalar and vectorial cases. Ada Math. 178 (1997), 1–37.Google Scholar
7Dacorogna, B. and Marcellini, P.. Cauchy–Dirichlet problem for first order nonlinear systems. J. Fund. Anal. 152(1998), 404–46.CrossRefGoogle Scholar
8Dret, H. Le. Sur les fonctions de matrices convexes et isotropes. C. R. Acad. Sci. Paris Sér. I 310 (1990), 617–20.Google Scholar
9Rockafellar, R. T.. Convex analysis (Princeton, NJ: Princeton University Press, 1970).CrossRefGoogle Scholar