On a Class of Linearizable Monge-Ampère Equations
- 10.2991/jnmp.19188.8.131.52How to use a DOI?
Monge-Ampère equations of the form, uxxuyy - u2 xy = F(u, ux, uy) arise in many areas of fluid and solid mechanics. Here it is shown that in the special case F = u4 yf(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 .
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Cite this article
TY - JOUR AU - D.J. Arrigo AU - J.M. Hill PY - 1998 DA - 1998/05/01 TI - On a Class of Linearizable Monge-Ampère Equations JO - Journal of Nonlinear Mathematical Physics SP - 115 EP - 119 VL - 5 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.19184.108.40.206 DO - 10.2991/jnmp.19220.127.116.11 ID - Arrigo1998 ER -