Elliptic and Parabolic Equations - Abstract

Roßmann, Jürgen

Estimates of the Green's matrix for the Stokes system in polyhedral domains

The talk is concerned with the Dirichlet problem for the Stokes system in a three-dimensional domain of polyhedral type. Estimates for the elements of the Green's matrix are obtained, where the majorants depend explicitly on the position of the arguments with respect to the edges and vertices. In the case of a convex polyhedral domain it follows in particular that [ big partial_x^alpha partial_xi^beta G_i,j(x,xi)big le c, x-xi ^-1-delta_i,4-delta_j,4- alpha - beta ] for $ alpha le 1-delta_i,4$, $ beta le 1-delta_j,4$. Moreover, Hölder estimates for the elements of Green's matrix and their derivatives hold.