Anisotropic fractional perimeters
By Monika Ludwig. 2013
81 citations recorded by the source corpus.
The anisotropic fractional $s$-perimeter with respect to a convex body $K$ in $\rn$ is shown to converge to the anisotropic perimeter with respect to the moment body of $K$ as $s\to 1^-$. A corresponding result is established for anisotropic fractional $s$-seminorms on $BV(\rn)$ (generalizing results of Bourgain, Brezis & Mironescu and D\'avila). The minimizers of the anisotropic fractional $s$-isoperimetric inequality with respect to $K$ are shown to converge to the moment body of $K$. Anisotropic fractional Sobolev inequalities are established.
View Paper: https://www.semanticscholar.org/paper/ce7300f55b05edac80cfd7b4d2b96835c1d22d1c
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- Lorenzo Brasco
- Erik Lindgren
- Enea Parini
- Monika Ludwig
- Cristiana De Filippis
- P. Garain
- Franz E. Schuster
- Christoph Haberl
Citations in the corpus
- The fractional Cheeger problem (2013, background): “We point out that the constant ωN−1 can be deduced from formula (4) in [27].”
- Anisotropic fractional Sobolev norms (2013, background): “r f ∈ Lp(Ω) in the sense that if f ∈ W1,p(Ω), then both sides of (5) are infinite. For p = 1, it follows from [2, Theorem 3’] that a corresponding result holds for f ∈ BV(Rn) (see also Davila [6]). In [19], the limiting behavior of fractional anisotropic Sobolev seminorms on BV(Rn) is discussed using”