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Linearizable Second Order Monge–Ampère Equations

✍ Scribed by Francesco Oliveri

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
176 KB
Volume
218
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we consider the second order Monge᎐Ampere equations in Ž . Ž . Ž . 1q1 , 2 q 1 , and 3 q 1 dimensions. We face the problem of reducing to linear form the first order systems that are equivalent to the given Monge᎐Ampere èquations.

When the coefficients are assumed constant there are introduced invertible point transformations, suggested by the invariance with respect to one-parameter Lie groups of point symmetries, allowing us to get linear equations. Moreover, the case of nonconstant coefficients is discussed and some linearizable classes of Monge᎐Ampere equations with coefficients depending on first order derivatives are characterized.

📜 SIMILAR VOLUMES

A symmetrization result for Monge–Ampère
A symmetrization result for Monge–Ampère type equations
✍ Barbara Brandolini; Cristina Trombetti 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 171 KB

## Abstract In this paper we prove some comparison results for Monge–Ampère type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)