The authors study the Hedge theory of the exterior differential operator d acting on q-forms on a smoothly bounded domain in RN+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 Visik and Eskin, and by Boutet de Monvel
Fontana, L., Krantz, S., Peloso, M. (1998). Hodge theory in the Sobolev topology for the de Rham complex. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 131(622).
Hodge theory in the Sobolev topology for the de Rham complex
FONTANA, LUIGI;
1998
Abstract
The authors study the Hedge theory of the exterior differential operator d acting on q-forms on a smoothly bounded domain in RN+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 Visik and Eskin, and by Boutet de Monvel
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