Monge cone

In the mathematical theory of partial differential equations (PDE), the Monge cone is a geometrical object associated with a first-order equation. It is named for Gaspard Monge. In two dimensions, let

be a PDE for an unknown real-valued function u in two variables x and y. Assume that this PDE is non-degenerate in the sense that $F_{u_x}$ and $F_{u_y}$ are not both zero in the domain of definition. Fix a point (x₀, y₀, z₀) and consider solution functions u which have

单词	Monge cone
释义	Monge cone 英语百科 Monge cone In the mathematical theory of partial differential equations (PDE), the Monge cone is a geometrical object associated with a first-order equation. It is named for Gaspard Monge. In two dimensions, let be a PDE for an unknown real-valued function u in two variables x and y. Assume that this PDE is non-degenerate in the sense that $F_{u_x}$ and $F_{u_y}$ are not both zero in the domain of definition. Fix a point (x₀, y₀, z₀) and consider solution functions u which have
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