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 Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 1/2, Pages 102–117 (Mi jmag485)

On complete convex solutions of the equation $\operatorname{spur}_m(z_{ij})=1$

V. N. Kokarev

Samara State University

Abstract: Let designation $\operatorname{spur}_m(z_{ij})=1$ stand for the sum of all principal $m$-order minors of matrix $(z_{ij})$, consisting of second derivatives of the function $z(x^1,…,x^n)$. Any complete convex class $C^{2\alpha}$ solution of the equation $\operatorname{spur}_m(z_{ij})=1$, ($2\le m<n$), will be a quadratic polynomial if the matrix $(z_{ij})$ eigenvalues are sufficiently close to each other.

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Citation: V. N. Kokarev, “On complete convex solutions of the equation $\operatorname{spur}_m(z_{ij})=1$”, Mat. Fiz. Anal. Geom., 3:1/2 (1996), 102–117

Citation in format AMSBIB
\Bibitem{Kok96} \by V.~N.~Kokarev \paper On complete convex solutions of the equation $\operatorname{spur}_m(z_{ij})=1$ \jour Mat. Fiz. Anal. Geom. \yr 1996 \vol 3 \issue 1/2 \pages 102--117 \mathnet{http://mi.mathnet.ru/jmag485} \zmath{https://zbmath.org/?q=an:0866.35027}