An integral operator related to the Stokes system in exterior domains
Paul Deuring · Mathematical Methods in the Applied Sciences · 1990
Abstract Consider a bounded domain Ω in ℝ3 with C2‐boundary ∂Ω. In [1] the Stokes problem in the exterior domain ℝ3/Ω, with resolvent parameter [λϵℂ\] − [∞,0], is solved by using the method of integral equations. However, for estimating the corresponding solutions in Lp norms, it turns out that a certain operator defined on the spaces Lr(∂Ω)3, for r ϵ]1, ∞[, has to be evaluated in the norm of Lr(∂Ω)3. This estimate is proved in the present paper.