Explicit characterisation of the fractional power spaces of the Dirichlet Laplacian and Stokes operators

TL;DR

This paper explicitly characterizes the fractional power spaces of the Dirichlet Laplacian and Stokes operators using real interpolation, providing accessible arguments despite the results being known.

Contribution

The paper offers an explicit and accessible characterization of fractional power spaces for key differential operators, enhancing understanding and potential applications.

Findings

Explicit fractional space descriptions for Dirichlet Laplacian and Stokes operators

Use of real interpolation theory for characterization

Accessible proofs despite existing results

Abstract

We identify explicitly the fractional power spaces for the $L^2$ Dirichlet Laplacian and Dirichlet Stokes operators using the theory of real interpolation. The results are not new, but we hope that our arguments are relatively accessible.