A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up

Giovanni E. Comi, Giorgio Stefani

We introduce the new space $B{V}^{\alpha }({\mathbb{R}}^n)$ of functions with bounded fractional variation in ${\mathbb{R}}^n$ of order $\alpha \in (0,1)$ via a new distributional approach exploiting…