Hodge theory in the Sobolev topology for the de Rham complex

Details Hodge theory in the Sobolev topology for the de Rham complex Hodge theory in the Sobolev topology for the de Rham complex

1996-01-22

arxiv.org/abs/math/9601208v1

Mathematics

Differential Geometry

Scientific paper

The authors study the Hodge theory of the exterior differential operator $d$ acting on $q$-forms on a smoothly bounded domain in $\RR^{N+1}$, and on the half space $\rnp$. 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 Vi\v{s}ik and Eskin, and by Boutet de Monvel.

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