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

2004/12/21 by Vladimir G. Maz'ya, Maz'ya, Vladimir G., Juergen Rossmann +1
Mathematics · Physics and Astronomy · #35J25 #35J55 #35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35J25 #msc:35J55 #msc:35Q30

paper · pdf · doi:10.48550/arxiv.math-ph/0412073

40 pages

arxiv created 2004/12/21 · arxiv updated 2009/12/01

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 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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