On blow-ups of sets with finite fractional variation

Giorgio Stefani

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arXiv · 2511.03854

On blow-ups of sets with finite fractional variation

Giorgio Stefani

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Abstract

Given $\alpha\in(0,1)$ and a set $E\subset\mathbb{R}^N$ with locally finite fractional $\alpha$-variation, we show that for $|D^\alpha\mathbf 1_E|$-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 $x$.

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Giorgio Stefani. 2025-11-05. On blow-ups of sets with finite fractional variation. https://arxiv.org/abs/2511.03854

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