Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Moreno

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

created by moreno on 15 Sep 2020


Published Paper

Inserted: 15 sep 2020
Last Updated: 15 sep 2020

Journal: Banach Centre Publications
Year: 2017

ArXiv: 1703.03944 PDF


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.


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