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Application of the Trace Inequality to the Poisson Equation

Authors:

Sadek Gala

Affiliation:

(1) Department of Mathematics, University of Mostaganem, Box. 227, Mostaganem, 27000, Algeria

Abstract:

The purpose of this paper is to show that solutions of the Poisson equation

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 : $D^{k} uin mathcal{M}left( overset{.}{H}^{1}rightarrow overset{.}{H}^{-1}right)$ for all $$k,leftvert krightvert =2$$

. 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.

Keywords:

Mathematics Subject Classificaitions (2000) 42B20 42B25

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