Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains

Details Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains

2004-12-21

arxiv.org/abs/math-ph/0412073v1

Physics

Mathematical Physics

40 pages

Scientific paper

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 sides of the polyhedron. The authors prove the existence of solutions in (weighted and non-weighted) $L_p$ Sobolev spaces and obtain regularity assertions for weak solutions. The results are based on point estimates of Green's matrix.

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