Weighted Lp theory of the Stokes and the bilaplacian operators in the half-space

We consider the Stokes and the bilaplacian equations in the half-space of Rn, n⩾2. Existence, uniqueness and smoothness of weak weighted Lp solutions are treated. We prove that these problems can be broken down into three or four Poisson-like problems. The importance of this decomposition is displayed through a short discussion on the numerical approximation of solutions by means of inverted finite elements method.