论文标题
非本地周长的渐近学
Asymptotics of non-local perimeters
论文作者
论文摘要
我们介绍了一个非本地周长的概念，该概念是通过$ \ m athbb {r}^d $在$ \ mathbb {r}^d $上定义的，该测量集成了$ 1 \ wedge | x | $。非本地周边的这种定义包括在文献中已经研究过的各种周长，包括分数周围和各向异性分数周围。本文的主要部分致力于研究非本地周围的渐近行为。作为直接应用，我们恢复了分数周围和各向异性分数周围的众所周知的收敛结果
We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on $\mathbb{R}^d$ which integrates the function $1\wedge |x|$. Such definition of non-local perimeter encompasses a wide range of perimeters which have been already studied in the literature, including fractional perimeters and anisotropic fractional perimeters. The main part of the article is devoted to the study of the asymptotic behaviour of non-local perimeters. As direct applications we recover well-known convergence results for fractional perimeters and anisotropic fractional perimeters
