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In the mathematical theory of partial differential equations, a Monge equation,[1] named after Gaspard Monge, is a first-order partial differential equation for an unknown function u in the independent variables x1,...,xn
that is a polynomial in the partial derivatives of u. Any Monge equation has a Monge cone.
Classically, putting u = x0, a Monge equation of degree k is written in the form
and expresses a relation between the differentials dxk. The Monge cone at a given point (x0, ..., xn) is the zero locus of the equation in the tangent space at the point.
The Monge equation is unrelated to the (second-order) Monge–Ampère equation.
References
edit- ^ "Monge method". evlm.stuba.sk. Retrieved 2022-10-16.
- Rozov, N. Kh. (1990). "Monge equation". In Hazewinkel, Michiel (ed.). Encyclopedia of Mathematics. Vol. 6. Kluwer Academic Publishers. ISBN 1-55608-005-0.