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.
Hodge theory in the Sobolev topology for the de Rham complex / L. Fontana, S.G. Krantz, M.M. Peloso. - In: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0065-9266. - :622(1998), pp. 1-99.
Hodge theory in the Sobolev topology for the de Rham complex
M.M. Peloso
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.Pubblicazioni consigliate
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