Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets. (English) Zbl 1435.46016
Summary: 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 mostly of 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.
MSC:
| 46B70 | Interpolation between normed linear spaces |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
interpolation of Banach spaces; (fractional) Sobolev spaces; traces and extensions of Sobolev functions; porous sets; measure density conditions; Hardy’s inequalityReferences:
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