Luigi Fontana

Hodge theory in the Sobolev topology for the de Rham complex

The authors study the Hodge theory of the exterior differential oper- ator d acting on q-forms on a smoothly bounded domain in R N+1 , and on the half space R N+1 + . The novelty is that the topology used is not an L 2 topology but a Sobolev topology. This strikingly alters the problem as compared to the classical setup. It gives rise to a boundary value problem belonging to a class of problems first introduced by Viysik and Eskin, and by Boutet de Monvel.

Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space

The authors study the Hodge theory of the exterior differential operator d acting on q-forms on a smoothly bounded domain in R, and on the half space R + . The novelty is that the topology used is not an L 2 topology but a Sobolev topology. This strikingly alters the problem as compared to the classical setup. It gives rise to a boundary value problem belonging to a class of problems first introduced by Vǐsik and Eskin, and by Boutet de Monvel.