Gelfand-Shilov Regularity of SG Boundary Value Problems

TL;DR

This paper establishes Gelfand-Shilov regularity for solutions of SG elliptic boundary value problems on unbounded domains, extending classical regularity results using advanced pseudo-differential operator techniques.

Contribution

It introduces new regularity results in Gelfand-Shilov spaces for SG elliptic boundary value problems on unbounded domains, utilizing Calderón projectors and recent developments in pseudo-differential operators.

Findings

Solutions exhibit Gelfand-Shilov regularity on unbounded domains.

Extension of classical Gevrey regularity results to the SG setting.

Application of Calderón projectors to SG boundary 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 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.