Gelfand-Shilov Regularity of SG Boundary Value Problems

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.