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arXiv · 2204.04178

Asymptotic behavior for anisotropic fractional energies

Julian Fernandez Bonder·Ariel Salort
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Abstract

In this paper we investigate the asymptotic behavior of anisotropic fractional energies as the fractional parameter $s\in (0,1)$ approaches both $s\uparrow 1$ and $s\downarrow 0$ in the spirit of the celebrated papers of Bourgain-Brezis-Mironescu \cite{BBM} and Maz'ya-Shaposhnikova \cite{MS}. Then, focusing con the case $s\uparrow 1$ we analyze the behavior of solutions to the corresponding minimization problems and finally, we also study the problem where a homogenization effect is combined with the localization phenomena that occurs when $s\uparrow 1$.

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Julian Fernandez Bonder, Ariel Salort. 2022-04-17. Asymptotic behavior for anisotropic fractional energies. https://arxiv.org/abs/2204.04178

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