Published.
Inserted: 7 feb 2018
Last Updated: 15 sep 2020
Journal: Complex Manifolds
Volume: 5
Number: 1
Pages: 26-88
Year: 2018
Doi: 10.1515/coma-2018-0003
Abstract:
In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n+1)-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a 30-hours Ph.D course given by two of the authors (GM and GM). As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.
Tags:
MSC2014-GEOGRAL