Weighted L-p-theory for vector potential operators in three-dimensional exterior domains

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. Copyright (c) 2015 John Wiley & Sons, Ltd.