The Poisson equation in homogeneous Sobolev spaces
We consider Poisson's equation in an n-dimensional exterior domain G(n≥2) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain Lq(G)-spaces there exists a solution in the homogeneous Sobolev space S2,q(G), containing functions being local i...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204308094 |
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| Summary: | We consider Poisson's equation in an n-dimensional exterior
domain G(n≥2) with a sufficiently smooth boundary. We
prove that for external forces and boundary values given in
certain Lq(G)-spaces there exists a solution in the
homogeneous Sobolev space S2,q(G), containing functions
being local in Lq(G) and having second-order derivatives in
Lq(G) Concerning the uniqueness of this solution we prove
that the corresponding nullspace has the dimension n+1, independent of q. |
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| ISSN: | 0161-1712 1687-0425 |