Rearrangements and the Maz'ya-Shaposhnikova limit: $\Gamma$-convergence for truncated interactions

Andrea Braides, Anneliese Defranceschi, Enrico Vitali

We give a proof of the $\Gamma$-liminf inequality for the Maz'ya--Shaposhni\-kova limit, as $s\to 0^{+}$, of the fractional Sobolev seminorm, based on spherical rearrangements. The key poi…