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Quasiconvex quadratic forms in two dimensions. (English) Zbl 0567.49007

Soient f et g deux formes quadratiques réelles sur \({\mathbb{R}}^ n\). L’auteur donne des conditions pour que f-\(\lambda\) g soit positive définie (resp. semidéfinie). Il retrouve en particulier le fait que si \(n=N=2\), alors, pour une forme quadratique, on a les equivalences: conditions de Legendre-Hadamard \(\Leftrightarrow\) polyconvexité \(\Leftrightarrow\) quasiconvexité.
Reviewer: H.Brezis

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
26B25 Convexity of real functions of several variables, generalizations
15A63 Quadratic and bilinear forms, inner products
90C25 Convex programming
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