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A full interpolation theory for Sobolev functions with smoothness between 0and 1 and vanishing trace on a part of the boundary of an open set isestablished. Geometric assumptions are of mostly measure theoretic nature andreach beyond Lipschitz regular domains. Previous results were limited toregular geometric configurations or Hilbertian Sobolev spaces. Sets with porousboundary and their characteristic multipliers on smoothness spaces play a majorrole in the arguments.

Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets