𝓡-boundedness for an integral operator in the half space and its application to the Stokes problems (Mathematical analysis of viscous incompressible fluid)

Abstract

In this paper, we give a sufficient condition for 𝓡-boundedness of an integral operator defined on the half-space. The assumption is simply bounded and holomorphic, which is easy to check. As applications, we derive resolvent estimate and maximal regularity for the Stokes equations with various boundary conditions. We can treat Dirichlet, Neumann and Robin boundary conditions in a unified manner.