International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 36, Pages 1909-1921
The Poisson equation in homogeneous Sobolev spaces
Fachbereich 17 Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str. 40, Kassel 34109, Germany
Received 9 August 2003
Copyright © 2004 Tatiana Samrowski and Werner Varnhorn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider Poisson's equation in an -dimensional exterior
domain with a sufficiently smooth boundary. We
prove that for external forces and boundary values given in
certain -spaces there exists a solution in the
homogeneous Sobolev space , containing functions
being local in and having second-order derivatives in
Concerning the uniqueness of this solution we prove
that the corresponding nullspace has the dimension , independent of .