E. Vitali

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

We give a proof of the $\Gamma$-liminf inequality for the Maz'ya--Shaposhni\-kova limit, as $s\to0^+$, of the fractional Sobolev seminorm, based on spherical rearrangements. The key point is that the rearrangements of a weakly convergent sequence are monotone radial profiles, which converge strongly by Helly's theorem;...