Gelfand–Shilov regularity of SG boundary value problems

Abstract

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 Calderón 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.