On blow-ups of sets with finite fractional variation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909900259459072 |
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| author | Stefani, Giorgio |
| author_facet | Stefani, Giorgio |
| contents | Given $α\in(0,1)$ and a set $E\subset\mathbb{R}^N$ with locally finite fractional $α$-variation, we show that for $|D^α\mathbf 1_E|$-a.e. $x$, every non-trivial tangent set of $E$ at $x$ with locally finite integer perimeter is a half-space oriented by the fractional inner unit normal of $E$ at $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On blow-ups of sets with finite fractional variation Stefani, Giorgio Analysis of PDEs Functional Analysis Primary 49Q15. Secondary 26A33, 28A75, 49Q20 Given $α\in(0,1)$ and a set $E\subset\mathbb{R}^N$ with locally finite fractional $α$-variation, we show that for $|D^α\mathbf 1_E|$-a.e. $x$, every non-trivial tangent set of $E$ at $x$ with locally finite integer perimeter is a half-space oriented by the fractional inner unit normal of $E$ at $x$. |
| title | On blow-ups of sets with finite fractional variation |
| topic | Analysis of PDEs Functional Analysis Primary 49Q15. Secondary 26A33, 28A75, 49Q20 |
| url | https://arxiv.org/abs/2511.03854 |