*Published Paper*

**Inserted:** 15 sep 2020

**Last Updated:** 15 sep 2020

**Journal:** Banach Centre Publications

**Year:** 2017

**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