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arXiv · 2410.17829

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

Andrea Kubin·Valerio Pagliari·Antonio Tribuzio
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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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Andrea Kubin, Valerio Pagliari, Antonio Tribuzio. 2024-10-23. Second-order asymptotics of fractional Gagliardo seminorms as $s\to1^-$ and convergence of the associated gradient flows. https://arxiv.org/abs/2410.17829

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