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Marcellini, Paolo

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

Appl. Math. Optimization 11, 183-189 (1984).
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

Cited in 22 Documents

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

Keywords:

quadratic forms in two dimensions; Legendre-Hadamard condition; polyconvexity; quasiconvexity
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\textit{P. Marcellini}, Appl. Math. Optim. 11, 183--189 (1984; Zbl 0567.49007)
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