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

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arxiv 2410.17829 v1 pith:EUF4BJOY submitted 2024-10-23 math.AP

Andrea Kubin , Valerio Pagliari , Antonio Tribuzio This is my paper · ORCID
classification math.AP
keywords flowsgradientfractionalgagliardosecond-orderassociatedasymptoticasymptotics
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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.

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