论文标题
各向异性分数能量的渐近行为
Asymptotic behavior for anisotropic fractional energies
论文作者
论文摘要
在本文中，我们研究了各向异性分数能量的渐近行为，作为分数参数$ s \ in（0,1）$的方法，均以$ s \ uparrow 1 $ 1 $和$ s \ downarrow 0 $在著名论文的精神上\ cite {ms}。 然后，将con con Case $ s \ uparrow 1 $ 1 $分析了解决相应最小化问题的解决方案的行为，最后，我们还研究了问题，其中均化效应与$ s \ uparrow 1 $时发生的本地化现象相结合。
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 $s\uparrow 1$.
