HODGE THEORY IN THE SOBOLEV TOPOLOGY FOR THE DE-RHAM COMPLEX

The authors study the Hedge theory of the exterior differential operat or d acting on q-forms on a smoothly bounded domain in RN+1, and on th e half space R-+(N+1). The novelty is that, the topology used is not a n L-2 topology but a Sobolev topology. This strikingly alters the prob lem as compared to the classical setup. It gives rise to a boundary va lue problem belonging to a class of problems first introduced by Visik and Eskin, and by Boutet de Monvel.