Second-order asymptotics of fractional Gagliardo seminorms as $s\to 1^{-}$ and convergence of the associated gradient flows

Andrea Kubin, Valerio Pagliari, Antonio Tribuzio

We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\to 1^{-}$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence re…