Lp estimates of solutions tomixed boundary value problems for the Stokes system in polyhedral domains
Vladimir Gilelevich Maz'ya, J. Roßmann · Mathematische Nachrichten · 2007
Abstract A mixed boundary value problem for the Stokes system in a polyhedral domain is considered. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the faces of the polyhedron. The authors prove the existence of solutions in (weighted and non‐weighted) Lp Sobolev spaces and obtain regularity assertions for weak solutions. The results are based on point estimates of Green's matrix. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)