General solutions of the Monge-Amp\`ere equation in n-dimensional space
Abstract
It is shown that the general solution of a homogeneous Monge-Amp\`ere equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ j∂ x0+Σk=1n-1 k ∂ j∂ xk=0 1 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Amp\`ere equation.
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