Trace of Homogeneous Fractional Sobolev Spaces on Strip-like Domains

Abstract

In this paper, we discuss the trace operator for homogeneous fractional Sobolev spaces over infinite strip-like domains. We determine intrinsic seminorms on the trace space that allow for a bounded right inverse. The intrinsic seminorm includes two features previously used to describe the trace of homogeneous Sobolev spaces, a relation between the two disconnected components of the trace and the screened Sobolev seminorm. However, unlike its homogeneous Sobolev space equivalent, fractional Sobolev spaces require a far screened Sobolev seminorm that captures the non-local properties of fractional Sobolev spaces. We study some basic relationships between this new far screened Sobolev space with previously discussed screened Sobolev spaces.