论文标题
$ c^{1，β} $开放式的具有多线性关键电位的区域分数拉普拉斯人的热内核估计值
Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, β}$ open sets
论文作者
论文摘要
令$ d $为$ \ mathbb {r}^d $，$α\ in（0，2）$，让$ \ mathcal {l}_α^d $是$ d $中的$α$稳定过程的生成器。在本文中，我们建立了$ \ Mathcal {l}_α^d-κ$的尖锐的双面热核的估计，其中$κ$是非负关键潜力，而$ d $是$ c^{1，β} $ open集，$β\ in（α-1）_+，1] $。比早期文献中关于分数拉普拉斯人的热核估计值的规律性弱。
Let $D$ be an open set of $\mathbb{R}^d$, $α\in (0, 2)$ and let $\mathcal{L}_α^D$ be the generator of the censored $α$-stable process in $D$. In this paper, we establish sharp two-sided heat kernel estimates for $\mathcal{L}_α^D-κ$, with $κ$ being a non-negative critical potential and $D$ being a $C^{1, β}$ open set, $β\in ((α-1)_+,1]$. The potential $κ$ can exhibit multi-singularities and our regularity assumption on $D$ is weaker than the regularity assumed in earlier literature on heat kernel estimates of fractional Laplacians.
