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

Autor: Moritz Egert, Sebastian Bechtel

Publikováno v: Journal of Fourier Analysis and Applications
Journal of Fourier Analysis and Applications, Springer Verlag, 2019, 25 (5), pp.2733-2781. ⟨10.1007/s00041-019-09681-1⟩

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 beyond Lipschitz reg

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https://hal.archives-ouvertes.fr/hal-01830708v3/file/Interpolation.pdf