RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zh. Mat. Fiz. Anal. Geom.: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (381 kB)
Full text: http:/.../abstract.php?uid=m03-0027r

Bibliographic databases:

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}