Degeneracy of the Characteristic Variety
Analysis of PDEs
2014-12-23 v3
Abstract
The characteristic variety plays an important role in the analysis of the solution space of partial differential equations and exterior differential systems. This article studies the linear span of this variety, measuring its dimension via an integrable extension of the original system. In the PDE case with locally constant characteristic variety, this extension yields a recursive version of Guillemin normal form, inducing a sequence of foliations on integral manifolds.
Keywords
Cite
@article{arxiv.1410.6947,
title = {Degeneracy of the Characteristic Variety},
author = {Abraham D. Smith},
journal= {arXiv preprint arXiv:1410.6947},
year = {2014}
}
Comments
See also "Constructing Involutive Tableaux with Guillemin Normal Form" arxiv:1410.7593 for some details. Version 2: No content changes; just fixed PDF font rendering for the arXiv and updated reference links. Version 3: Added two sections with examples