  This article proves the well posedness of the boundary value problemthat
arises when PML algorithms are applied to Pauli's equationswith a three
dimensional rectangle as computational domain. The absorptionsare positive near
the boundary and zero far from the boundary so are always x-dependent. At the
flat parts of the boundary of the rectangle, the natural absorbing boundary
conditions are imposed.The difficulty addressed is the analysis of the
resulting variable coeffi-cient problem on the rectanglar solid with its edges
and corners. TheLaplace transform is analysed. It turns on the analysis of a
boundaryvalue problem formally obtained by complex stretching. Existence
isproved by deriving a boundary value problems for a complex stretchedHelmholtz
equation on smoothed domains. This is the first stabilityproof with x-dependent
absorptions on a bounded domain whoseboundary is not smooth.
