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

Calculus of Variations and Geometric Measure Theory

A. Kubin - V. Pagliari - A. Tribuzio

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

created by kubin on 24 Oct 2024
modified by tribuzio on 04 Dec 2025

[BibTeX]

Published Paper

Inserted: 24 oct 2024
Last Updated: 4 dec 2025

Journal: Fractional Calculus and Applied Analysis
Year: 2025
Doi: 10.1007/s13540-025-00472-8

Abstract:

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.