Journal of Nonlinear Mathematical Physics

Volume 5, Issue 2, May 1998, Pages 115 - 119

On a Class of Linearizable Monge-Ampère Equations

Authors
D.J. ARRIGO, J.M. HILL
Corresponding Author
D.J. ARRIGO
Available Online 1 May 1998.
DOI
https://doi.org/10.2991/jnmp.1998.5.2.1How to use a DOI?
Abstract
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 [7].
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
5 - 2
Pages
115 - 119
Publication Date
1998/05
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1998.5.2.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - D.J. ARRIGO
AU  - J.M. HILL
PY  - 1998
DA  - 1998/05
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.1998.5.2.1
DO  - https://doi.org/10.2991/jnmp.1998.5.2.1
ID  - ARRIGO1998
ER  -