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

Vladimir G. Maz'ya·Juergen Rossmann
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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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Vladimir G. Maz'ya, Juergen Rossmann. 2004-12-21. Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains. https://arxiv.org/abs/math-ph/0412073

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