Trace and extension operators for fractional Sobolev spaces with variable exponent

TL;DR

This paper investigates the properties of trace and extension operators in fractional Sobolev spaces with variable exponents, establishing the existence of a linear extension operator under specific regularity conditions.

Contribution

It introduces a new linear extension operator for fractional Sobolev spaces with variable exponents, expanding the theoretical framework for these function spaces.

Findings

Existence of a linear extension operator under certain regularity assumptions

Extension operator preserves fractional Sobolev space properties

Advances understanding of variable exponent Sobolev spaces

Abstract

We show that, under certain regularity assumptions, there exists a linear extension operator.