  We show that the solutions of SG elliptic boundary value problems defined on
the complement of compact sets or on the half-space have some regularity in
Gelfand-Shilov spaces. The results are obtained using classical results about
Gevrey regularity of elliptic boundary value problems and Calder\'on projectors
techniques adapted to the SG case. Recent developments about Gelfand-Shilov
regularity of SG pseudo-differential operators on $\mathbb{R}^{n}$ appear in an
essential way.
