On blow-ups of sets with finite fractional variation

Abstract

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

8 pages. Minor improvements