Monge cone
（重定向自Characteristic 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}](/Images/godic/202501/04/024d28131ced5ab0ab1f583f0d681efd3446.png")
and ![F_{u_y}](/Images/godic/202501/04/92eefaad14db4b5cc2a8814274d6445a3446.png")
are not both zero in the domain of definition. Fix a point (x0, y0, z0) and consider solution functions u which have