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Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 1/2, Pages 27–33 (Mi jmag479)  

Weakly connected systems of Monge–Amper elliptic equations and the problem of existence of $2$-surface in $E^{k+2}$ with given Killing–Lipschitz curvatures with respect to $k$ normal vectors

B. E. Kantor, V. M. Vereshchagin

Murmansk State Pedagogical University

Abstract: A surface $z^i=u^i(x,y)$, $i=1,…,k$, projected regularly onto a domain $\Omega$ of the $(x,y)$-plane is considered in a $(k+2)$-dimensional Euclidean space. We introduce natural unit vectors $\xi_i$ directed along the vectors $(u^i_x,u^i_y,0,…,0,-1,0,…)$, $i=1,…,k$, where $-1$ is in the $(2+i)$-coordinate place, and the Killing–Lipschitz curvatures $K^i (x, y)$ with respect to these normal vectors. The problem of construction of a surface with given positive functions $K^i(x,y)$ and a given boundary value $u^i|_{\partial\Omega}=\varphi^i(\sigma)$, where $\sigma$ is the parameter in the curve $\partial\Omega$, is solved.

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Received: 09.06.1994

Citation: B. E. Kantor, V. M. Vereshchagin, “Weakly connected systems of Monge–Amper elliptic equations and the problem of existence of $2$-surface in $E^{k+2}$ with given Killing–Lipschitz curvatures with respect to $k$ normal vectors”, Mat. Fiz. Anal. Geom., 3:1/2 (1996), 27–33

Citation in format AMSBIB
\Bibitem{KanVer96}
\by B.~E.~Kantor, V.~M.~Vereshchagin
\paper Weakly connected systems of Monge--Amper elliptic equations and the problem of existence of
$2$-surface in $E^{k+2}$ with given Killing--Lipschitz curvatures with respect to
$k$~normal vectors
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 1/2
\pages 27--33
\mathnet{http://mi.mathnet.ru/jmag479}
\zmath{https://zbmath.org/?q=an:0867.53004}


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