Positivity

, Volume 12, Issue 2, pp 289–312 | Cite as

Application of the Trace Inequality to the Poisson Equation

  • Sadek Gala
Article
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Abstract

The purpose of this paper is to show that solutions of the Poisson equation
$$-\Delta u=f$$
where f be a complex-valued distribution on \({\mathbb{R}}^{d}\), d ≥ 3 and \(f{\in} {\mathcal{M}}\left( \overset{.}{H}^{1}{\rightarrow} \overset{.}{H} ^{-1}\right) \) satisfy the coercivity property : \(D^{k} u\in \mathcal{M}\left( \overset{.}{H}^{1}\rightarrow \overset{.}{H}^{-1}\right)\) for all \(k,\left\vert k\right\vert =2\) . The coercivity of this equation is well studied by Maz’ ya and Verbitsky [14] in the case where f belongs to the class of positive Borel measures.

Mathematics Subject Classificaitions (2000)

42B20 42B25 

Keywords

Poisson equation multiplier spaces coercivity criterion distributions 
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Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Sadek Gala
    • 1
  1. 1.Department of MathematicsUniversity of MostaganemMostaganemAlgeria

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