Weighted \(L^{p}\)-theory for vector potential operators in three-dimensional exterior domains (Q2814061)
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scientific article; zbMATH DE number 6594867
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted \(L^{p}\)-theory for vector potential operators in three-dimensional exterior domains |
scientific article; zbMATH DE number 6594867 |
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17 June 2016
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vector potential
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Laplace equations
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Sobolev inequalities
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Helmholtz decomposition
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weighted Sobolev spaces
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unbounded domains
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Weighted \(L^{p}\)-theory for vector potential operators in three-dimensional exterior domains (English)
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The authors make use of weighted Sobolev spaces to prove existence and regularity results concerning the following elliptic system NEWLINE\[NEWLINE u=\mathrm{curl }\psi, \text{ and }\operatorname{div}\psi=0\text{ in }\Omega, NEWLINE\]NEWLINE with suitable boundary conditions, where \(\Omega\) is an unbounded domain in \(\mathbb{R}^3\) with Lipschitz boundary and whose complement is simply connected. They also prove regularity results for the Dirichlet and Neumann Laplacian on unbounded domains, and for the Helmholtz decomposition of vectors.
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