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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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References:
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