Maximal $L^p$-$L^q$ regularity for the Stokes problem with Navier-type boundary conditions

TL;DR

This paper establishes maximal $L^p$-$L^q$ regularity for solutions of the Stokes problem with Navier boundary conditions in bounded domains, extending prior work to more general domain topologies.

Contribution

It extends previous maximal regularity results for the Stokes problem to include Navier boundary conditions in non-simply connected domains.

Findings

Maximal $L^p$-$L^q$ regularity proved for strong, weak, and very weak solutions.

Results apply to inhomogeneous Stokes problem with Navier boundary conditions.

Extends previous results to more general domain topologies.

Abstract

Maximal $L^p$-$L^q$ regularity is proved for the strong, weak and very weak solutions of the inhomogeneous Stokes problem with Navier-type boundary conditions in a bounded domain $\Omega$, not necessarily simply connected. This extends previous results of the authors (2017).