An introduction to completely exceptional $2^{\textrm{nd}}$ order scalar PDEs
Differential Geometry
2017-07-07 v2
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 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.
Cite
@article{arxiv.1703.03944,
title = {An introduction to completely exceptional $2^{\textrm{nd}}$ order scalar PDEs},
author = {Giovanni Moreno},
journal= {arXiv preprint arXiv:1703.03944},
year = {2017}
}
Comments
14 pages, 3 figures, slightly revised, to appear on Banach Centre Publications