On a Class of Linearizable Monge-Ampère Equations

Monge-Ampère equations of the form, uxxuyy − u 2 xy = F (u, ux, uy) arise in many areas of fluid and solid mechanics. Here it is shown that in the special case F = u y f(u, ux/uy), where f denotes an arbitrary function, the Monge-Ampère equation can be linearized by using a sequence of Ampère, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7].