Abstract

In this paper we are interested in functions defined, on a set of matrices, by the mean of quadratic forms and we compute the rank-one-convex, quasiconvex, polyconvex and convex envelopes of these functions. For that, and for a given quadratic form, we prove, in a first part, some general decomposition results for matrices, with a rank-one-compatibility condition. We also study the James-Ericksen stored energy function.

Author information

Contact details are reproduced from the original publication and may be historical.

M. Bousselsal

Département de Mathématiques, Ecole Normale Supérieure Vieux Kouba 16050 Algiers, Algeria.

B. Brighi

Centre d’Analyse Non Linéaire, Département de Mathématiques, URA-CNRS 399, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France

Keywords

  • rank-one-convex
  • quasiconvex
  • envelope
  • quadratic form
  • James-Ericksen function
  • Pipkin’s formula

Suggested citation

M. Bousselsal, B. Brighi. “Rank-One-Convex and Quasiconvex Envelopes for Functions Depending on Quadratic Forms.” Journal of Convex Analysis 4 (1997), No. 2, 305–319. https://doi.org/10.68381/jca04016

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 1997. Rights now held by Banach Press.