Submitted Paper

Inserted: 6 nov 2025
Last Updated: 13 nov 2025

Year: 2025

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 $x$.

Keywords: blow-up, Fractional Gradient, tangent measure, fractional variation, half-space

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• Stefani - On blow-ups of sets with finite fractional variation