Anisotropic fractional Sobolev norms
By Monika Ludwig. 2013
66 citations recorded by the source corpus.
Abstract Bourgain, Brezis & Mironescu showed that (with suitable scaling) the fractional Sobolev s -seminorm of a function f ∈ W 1 , p ( R n ) converges to the Sobolev seminorm of f as s → 1 − . The anisotropic s -seminorms of f defined by a norm on R n with unit ball K are shown to converge to the anisotropic Sobolev seminorm of f defined by the norm with unit ball Z p ⁎ K , the polar L p moment body of K . The limiting behavior for s → 0 + is also determined (extending results by Mazʼya & Shaposhnikova).
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/f40debfc45ac2055c0f03ad0b923f21799097281
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In Applied Mathematics
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- L. Pick
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- Robert J. Berman
In Numerical Analysis
Citations in the corpus
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