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In this paper we describe an interpolation result for the Sobolev spaces      H 0 s ( Ω  ) H_0^s(\Omega )       where      Ω  \Omega       is a bounded domain with a Lipschitz boundary. This result is applied to derive discrete norm estimates related to multilevel preconditioners and multigrid methods in the finite element method. The estimates are valid for operators of order 2 m  with Dirichlet boundary conditions.

Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory