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An introduction to completely exceptional second order scalar partial differential equations

Volume 113 / 2017

Giovanni Moreno Banach Center Publications 113 (2017), 275-289 MSC: 35A30, 35L15, 35L67, 53D10, 58A30, 14M15. DOI: 10.4064/bc113-0-15

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 second order (nonlinear) PDEs, he also proved that this class reduces to the class of Monge–Ampère equations. We review here, against a unified geometric background, the notion of complete exceptionality, the definition of a Monge–Ampère equation, and the interesting link between them.

Authors

  • Giovanni MorenoDepartment of Mathematical Methods in Physics
    University of Warsaw
    ul. Pasteura 5
    02-093 Warszawa, Poland
    e-mail

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