Universal prolongation of linear partial differential equations on filtered manifolds

Katharina Neusser

Address: Faculty of Mathematics, University of Vienna Nordbergstra├če 15, A-1090 Wien, Austria

E-mail: katharina.neusser@univie.ac.at

Abstract: The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.

AMSclassification: primary 35N05; secondary 58A20, 58A30, 53D10, 58J60.

Keywords: prolongation, partial differential equations, filtered manifolds, contact manifolds, weighted jet bundles.