Necessary and Sufficient Conditions for the Maz'ya-Shaposhnikova Formula in (Fractional) Sobolev Spaces

Elisa Davoli, Giovanni Di Fratta, Rossella Giorgio +1

We investigate the asymptotic behavior, as $\epsilon \to 0$, of nonlocal functionals $$ \mathcal{F}_{\varepsilon}(u) = \iint_{\mathbb{R}^N\times\mathbb{R}^N} ρ_{\varepsilon}(y-x…