Louati H.,Laboratoire Of Mathematiques Of Sfax Faculte Des Science Of Sfax Tunisie Route Of Soukra Km 35 Bp N Sfax 1171 3000 Tunisia |
Meslameni M.,Laboratoire Of Mathematiques Of Sfax Faculte Des Science Of Sfax Tunisie Route Of Soukra Km 35 Bp N Sfax 1171 3000 Tunisia |
Razafison U.,University of Franche Comte
Mathematical Methods in the Applied Sciences | Year: 2015
In the present paper, we study the vector potential problem in exterior domains of R3. Our approach is based on the use of weighted spaces in order to describe the behavior of functions at infinity. As a first step of the investigation, we prove important results on the Laplace equation in exterior domains with Dirichlet or Neumann boundary conditions. As a consequence of the obtained results on the vector potential problem, we establish useful results on weighted Sobolev inequalities and Helmholtz decompositions of weighted spaces. © 2015 John Wiley & Sons, Ltd.