Anisotropic Fractional Sobolev Norms

2013/04/02 by Monika Ludwig · 1 citation
Mathematics · #math.FA #math.AP #msc:46E35 #msc:52A20

paper · pdf · doi:10.1016/j.aim.2013.10.024

published as Advances in Mathematics 252, 150 - 157 (2014)

arxiv created 2013/04/02 · arxiv updated 2014/10/22

Abstract

Bourgain, Brezis & Mironescu showed that (with suitable scaling) the fractional Sobolev s-seminorm of a function f∈ W^1,p(\rn) converges to the Sobolev seminorm of f as s→ 1^-. The anisotropic s-seminorms of f defined by a norm on \rn with unit ball K are shown to converge to the anisotropic Sobolev seminorm of f defined by the norm with unit ball \ompd K, the polar L_p moment body of K. The limiting behavior for s→ 0⁺ is also determined (extending results by Maz'ya & Shaposhnikova).

Cited by

• Asymmetric anisotropic fractional Sobolev norms

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