Second-order asymptotics of fractional Gagliardo seminorms as $s\to1^-$ and convergence of the associated gradient flows

Andrea Kubin, Valerio Pagliari, Antonio Tribuzio

Published 2024-10-23Version 1

We study the second-order asymptotic expansion of the $s$-fractional Gagliardo seminorm as $s\to1^-$ in terms of a higher order nonlocal functional. We prove a Mosco-convergence result for the energy functionals and that the $L^2$-gradient flows of the energies converge to the $L^2$-gradient flows of the Mosco-limit.