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

Sebastian Bechtel, Moritz Egert

Published 2018-07-06Version 1

A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach far beyond Lipschitz regular domains. Previous results were limited to very regular geometric configurations or Hilbert Sobolev spaces.