Level sets of fractional Sobolev functions

Camillo De Lellis, Ming-Yuan Chang, Svitlana Mayboroda

We prove a coarea-type result for scalar functions $f$ in fractional Sobolev spaces $W^{s,p}(\Omega )$ with $\Omega \subset {\mathbb{R}}^n$, $0<s<1$, and $1\le p<\infty$. Our theorem shows t…