Monge-Ampère equation

From Wikipedia, the free encyclopedia

A Monge-Ampère equation is a second order scalar equation in the plane. Given two independent variables x,y and one dependent variable z we write partial derivatives with notations

p = z_x,q = z_y,r = z_xx,s = z_xy,t = z_yy.

A Monge-Ampère equation can be written in local coordinates as

a(rt − s²) + br + cs + dt + e = 0

where a,b,c,d,e are functions depending on the first order variables x,y,z,p,q only.

[edit] See also

• Gaspard Monge
• André-Marie Ampère
• Transportation theory

[edit] External link

• Weisstein, Eric W., Monge-Ampère Differential Equation at MathWorld.