An elliptic boundary problem in a half–space

The spectral theory for general non–selfadjoint elliptic boundary problems involving a discontinuous weight function has been well developed under certain restrictions concerning the weight function. In the course of extending the results so far established to a more general weight function, there arises the problem of establishing, in an L p Sobolev space setting, the existence of and a priori estimates for solutions for a boundary problem for the half–space ℝ n + involving a weight function which vanishes at the boundary x n = 0. In this paper we resolve this problem.