International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 36, Pages 1909-1921

The Poisson equation in homogeneous Sobolev spaces

Tatiana Samrowski and Werner Varnhorn

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 n-dimensional exterior domain G(n2) 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.