Elisa Davoli

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math.AP2026

Closing the gap: Maz'ya-Shaposhnikova and asymptotics of fractional perimeters

Elisa Davoli, Alberto Fanizza, Marco Picerni

We prove a generalization of the Maz'ya-Shaposhnikova formula in the case $p = 2$ for functions that may not belong to $L^{2} (R^{d})$ and, thus, might not vanish at infinity.…

math.AP2025

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 $ε \to 0$ , of nonlocal functionals $$ \mathcal{F}_{\varepsilon}(u) = \iint_{\mathbb{R}^N\times\mathbb{R}^N} ρ_{\varepsilon}(y-x…