Sur L’étude de quelques propriétés Fonctionnelles des espaces de Sobolev à poids et Application à des EDP de type elliptique

Abstract

The objective of this thesis are mutliple. The first objective is to provesome functional properties of a family of weighted Sobolev spaces. In particu-lar, we prove some useful identities concerning these spaces and we comparesome of them. The second objective is to study a system of Navier-Stokesequations which describe the motion of a fluid around a rotating obstacle.And finally, we propose a new spectral method for solving elliptic problemsin the whole space. The method is based on the use of an appropriate familyof rational functions