DIRICHLET AND NEUMANN EXTERIOR PROBLEMS FOR THE N-DIMENSIONAL LAPLACEOPERATOR AN APPROACH IN WEIGHTED SOBOLEV SPACES

This paper solves Dirichlet and Neumann problems for the Laplace opera tor in exterior domains of R(n). The behaviours at infinity of the dat a and the solution are determined by setting each problem in weighted Sobolev spaces, that extend the classical W-m,W-p spaces and are very well adapted to the theoretical and numerical solution of problems inv olving the Laplace operator.