Memoirs of the American Mathematical Society 1998; 100 pp; softcover Volume: 131 ISBN10: 0821808303 ISBN13: 9780821808306 List Price: US$45 Individual Members: US$27 Institutional Members: US$36 Order Code: MEMO/131/622
 In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the \(L^2\) topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. Features:  a good introduction to elliptic theory, pseudodifferential operators, and boundary value problems
 theorems completely explained and proved
 new geometric tools for differential analysis on domains and manifolds
Readership Graduate students, research mathematicians, control theorists, engineers and physicists working in boundary value problems for elliptic systems. Table of Contents  Preliminaries
 The problem on the half space
 The case of smoothly bounded domains
