Hodge Theory in the Sobolev Topology for the De Rham Complex - Memoirs of the American Mathematical Society UK Ed. edition

Treats the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L^2$ topology. This study takes place on both the upper half space and on a smoothly bounded domain. It also gives an introduction to elliptic theory, pseudo-differential operators, and boundary value problems.