# An introduction to completely exceptional $2^{\textrm{nd}}$ order scalar PDEs

created by moreno on 15 Sep 2020

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Published Paper

Inserted: 15 sep 2020
Last Updated: 15 sep 2020

Journal: Banach Centre Publications
Year: 2017

ArXiv: 1703.03944 PDF

Abstract:

In his 1954 paper about the initial value problem for 2D hyperbolic nonlinear PDEs, P. Lax declared that he had "a strong reason to believe" that there must exist a well-defined class of "not genuinely nonlinear" nonlinear PDEs. In 1978 G. Boillat coined the term "completely exceptional" to denote it. In the case of $2^{\textrm{nd}}$ order (nonlinear) PDEs, he also proved that this class reduces to the class of Monge-Amp\ere equations. We review here, against a unified geometric background, the notion of complete exceptionality, the definition of a Monge-Amp\ere equation, and the interesting link between them.

Tags: MSC2014-GEOGRAL

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