2017/08/09 by Eshkobilov, Olimjon, Manno, Gianni, Moreno, Giovanni +1
#32C15 #35A30 #35K96 #53C30 #53C55 #53D05 #53D10 #58A20 #58A30 #58J70 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1708.02718
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.