A note on the fractional perimeter and interpolation
(2017) Comptes rendus - Mathématique — Vol. 355, n° 9, p. 960-965 (2017)
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- Abstract
- 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 Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces W^{alpha, 1} of order 0 < alpha < 1.
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Ponce, A., & Spector, D. (2017). A note on the fractional perimeter and interpolation. Comptes rendus - Mathématique, 355(9), 960-965. https://doi.org/10.1016/j.crma.2017.09.001 (Original work published 2017)