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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| _version_ | 1832554467136897024 |
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| author | Tatiana Samrowski Werner Varnhorn |
| author_facet | Tatiana Samrowski Werner Varnhorn |
| author_sort | Tatiana Samrowski |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-eebd2ad25b9d4697a9a1db71ab0103d7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eebd2ad25b9d4697a9a1db71ab0103d72025-02-03T05:51:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004361909192110.1155/S0161171204308094The Poisson equation in homogeneous Sobolev spacesTatiana Samrowski0Werner Varnhorn1Fachbereich 17 Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str. 40, Kassel 34109, GermanyFachbereich 17 Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str. 40, Kassel 34109, GermanyWe 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.http://dx.doi.org/10.1155/S0161171204308094 |
| spellingShingle | Tatiana Samrowski Werner Varnhorn The Poisson equation in homogeneous Sobolev spaces International Journal of Mathematics and Mathematical Sciences |
| title | The Poisson equation in homogeneous Sobolev spaces |
| title_full | The Poisson equation in homogeneous Sobolev spaces |
| title_fullStr | The Poisson equation in homogeneous Sobolev spaces |
| title_full_unstemmed | The Poisson equation in homogeneous Sobolev spaces |
| title_short | The Poisson equation in homogeneous Sobolev spaces |
| title_sort | poisson equation in homogeneous sobolev spaces |
| url | http://dx.doi.org/10.1155/S0161171204308094 |
| work_keys_str_mv | AT tatianasamrowski thepoissonequationinhomogeneoussobolevspaces AT wernervarnhorn thepoissonequationinhomogeneoussobolevspaces AT tatianasamrowski poissonequationinhomogeneoussobolevspaces AT wernervarnhorn poissonequationinhomogeneoussobolevspaces |