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Paper detail

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

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 beyond Lipschitz regular domains. Previous results were limited to regular geometric configurations or Hilbertian Sobolev spaces. Sets with porous boundary and their characteristic multipliers on smoothness spaces play a major role in the arguments.

preprint2021arXivOpen access
Sebastian BechtelMoritz Egert
math.APmath.CA
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Sebastian BechtelMoritz Egert

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