On a resolvent estimate of the Stokes equation on an infinite layer.
The authors establish the weak solvability of the title problem, and prove standard \(L_p\) estimates for the solution. The proof is based on a partial Fourier transform which reduces the original problem to a two-point boundary value problem for a system of ordinary differential equations with parameter. Then an application of Agmon-Douglis-Nirenberg type estimates of singular integrals provides the desired result.
scientific article; zbMATH DE number 1943321