Providence, R.I. : American Mathematical Society, 1998.
Book — viii, 100 p. ; 26 cm.
Preliminaries The problem on the half space The case of smoothly bounded domains.
(source: Nielsen Book Data)
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. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds. (source: Nielsen Book Data)