  The Nahm pole boundary condition for certain gauge theory equations in four
and five dimensions is defined by requiring that a solution should have a
specified singularity along the boundary. In the present paper, we show that
this boundary condition is elliptic and has regularity properties analogous to
more standard elliptic boundary conditions. We also establish a uniqueness
theorem for the solution of the relevant equations on a half-space with Nahm
pole boundary conditions. These results are expected to have a generalization
involving knots, with applications to the Jones polynomial and Khovanov
homology.
