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Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space. (English) Zbl 0855.35034
Summary: The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied. As a result, a new elliptic boundary value problem is obtained. Next, the Hodge theory of the $$\overline\partial$$-Neumann problem in the Sobolev topology is studied. A new $$\overline\partial$$-Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived.
##### MSC:
 35J25 Boundary value problems for second-order elliptic equations 58A14 Hodge theory in global analysis 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs 58J10 Differential complexes 35S15 Boundary value problems for PDEs with pseudodifferential operators
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