Hodge Theory in the Sobolev Topology for the De Rham Complex
نویسندگان
چکیده
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.
منابع مشابه
Hodge Theory in the Sobolev Topology for the De Rham Complex on a Smoothly Bounded Domain in Euclidean Space
The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied. As a result, a new elliptic boundaryvalue problem is obtained. Next, the Hodge theory of the @-Neumann problem in the Sobolev topology is studied. A new @-Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived. The classical Hodge theory on a domain in R N+1 (or, more g...
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