The Poisson equation in homogeneous Sobolev spaces

Tatiana Samrowski and Werner Varnhorn

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-13

Abstract:

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 L q ( G ) -spaces there exists a solution in the homogeneous Sobolev space S 2 , q ( G ) , containing functions being local in L q ( G ) and having second-order derivatives in L q ( G ) Concerning the uniqueness of this solution we prove that the corresponding nullspace has the dimension n + 1 , independent of q .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:619871

DOI: 10.1155/S0161171204308094

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