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

[BibTeX]

preprint

Inserted: 24 oct 2024

Year: 2024

ArXiv: 2410.17829 PDF

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.