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| Content Provider | Springer Nature Link |
|---|---|
| Author | Ma, Dan |
| Copyright Year | 2014 |
| Abstract | Bourgain, Brezis, and Mironescu showed that (with suitable scaling) the fractional Sobolev s-seminorm of a function $${f \in W^{1,p}(\mathbb{R}^n)}$$ converges to the Sobolev seminorm of f as $${s\rightarrow1^-}$$ . Ludwig introduced the anisotropic fractional Sobolev s-seminorms of f defined by a norm on $${\mathbb{R}^n}$$ with unit ball K and showed that they converge to the anisotropic Sobolev seminorm of f defined by the norm whose unit ball is the polar L p moment body of K, as $${s \rightarrow 1^-}$$ . The asymmetric anisotropic s-seminorms are shown to converge to the anisotropic Sobolev seminorm of f defined by the Minkowski functional of the polar asymmetric L p moment body of K. |
| Ending Page | 175 |
| Page Count | 9 |
| Starting Page | 167 |
| File Format | |
| ISSN | 0003889X |
| e-ISSN | 14208938 |
| Journal | Archiv der Mathematik |
| Issue Number | 2 |
| Volume Number | 103 |
| Language | English |
| Publisher | Springer Basel |
| Publisher Date | 2014-08-23 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems Convex sets in $n$ dimensions (including convex hypersurfaces) L p moment body Fractional sobolev norm Mathematics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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