A note on the fractional perimeter and interpolation

Autor: Ponce, Augusto C., Spector, Daniel

Publikováno v: C. R. Math. Acad. Sci. Paris 355 (2017), no. 9, 960-965

We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the H

Externí odkaz: http://arxiv.org/abs/1707.06001

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9109b19ff8f389018ecb0727ee3051df
https://hal.archives-ouvertes.fr/hal-01830708v3/file/Interpolation.pdf

Interpolation of Morrey-Campanato and Related Smoothness Spaces

Autor: Winfried Sickel, Dachun Yang, Wen Yuan

In this article, the authors study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e.\,g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the $

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64300f2e915570b84e62ef208df4e145
http://arxiv.org/abs/1406.0906