General solutions of the Monge-Ampère equation in $n$-dimensional space

Details General solutions of the Monge-Ampère equation in $n$-dimensional space General solutions of the Monge-Ampère equation in $n$-dimensional space

1994-03-22

arxiv.org/abs/hep-th/9403134v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

10.1016/0393-0440(94)00035-3

It is shown that the general solution of a homogeneous Monge-Amp\`{e}re equation in $n$-dimensional space is closely connected with the exactly (but only implicitly) integrable system \frac {\partial \xi_{j}}{\partial x_0}+\sum_{k=1}^{n-1} \xi_{k} \frac {\partial \xi_{j}}{\partial x_{k}}=0 \label{1} Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Amp\`{e}re equation.

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