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On a class of linearizable Monge-Amp\`ere equations

Daniel J. Arrigo·James M. Hill
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Abstract

Monge-Amp\`ere equations of the form, $u_{xx}u_{yy}-u_{xy}^2=F(u,u_x,u_y)$ arise in many areas of fluid and solid mechanics. Here it is shown that in the special case $F=u_y^4f(u, u_x/u_y)$, where $f$ denotes an arbitrary function, the Monge-Amp\`ere equation can be linearized by using a sequence of Amp\`ere, 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].

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Daniel J. Arrigo, James M. Hill. 1998-04-01. On a class of linearizable Monge-Amp\`ere equations. https://doi.org/10.2991/jnmp.1998.5.2.1

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