Stormark O. Lie's Structural Approach to PDE Systems

Cambridge University Press, 2000. — 590 p. — Series: Encyclopedia of Mathematics and its Applications (Book 80) OCR
ISBN10: 0521880157 ISBN13: 978-0521780889.Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear PDE systems without using power series techniques, it describes a general approach to PDE systems based on ideas developed by Lie, Cartan and Vessiot. The central theme is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.