Spectral properties for layer potentials associated to the Stokes equation in Lipschitz domains

In this paper, we consider the spectral properties of the double layer potentials K and \({\tilde{K}}\) related to the traction boundary value problem and the slip boundary value problem, respectively, of the Stokes equations in a bounded Lipschitz domain Ω in R ⁿ . We show the invertibility of λI ? K and \({\lambda I - \tilde{K}}\) in L ²(?Ω) for \({\lambda \in {\bf R}{\setminus} -\frac 12, \frac12]}\). As an application, we study the transmission problems of the Stokes equations.