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L p estimates of solutions tomixed boundary value problems for the Stokes system in polyhedral domains
Author(s) -
Maz'ya V.,
Rossmann J.
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610513
Subject(s) - mathematics , polyhedron , dirichlet distribution , sobolev space , stokes problem , domain (mathematical analysis) , neumann boundary condition , boundary value problem , boundary (topology) , mathematical analysis , matrix (chemical analysis) , pure mathematics , combinatorics , physics , materials science , finite element method , composite material , thermodynamics
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) L p 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)