论文标题
关于一般域上的分数拉普拉斯方程的dirichlet问题
On the Dirichlet problem for fractional Laplace equation on a general domain
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {r}^n $中的一般有限域上的分数拉普拉斯（Poisson）方程的差异问题。格林的功能和泊松内核是我们研究所需的重要工具。我们首先通过Perron方法的应用确定Green功能的存在。之后，泊松内核是根据绿色功能构建的。证明了格林功能和泊松仁的几个重要特性。最后，我们表明，在给定条件下的分数拉普拉斯方程（泊松）方程的解决方案必须是独一无二的，并且由我们的绿色功能和泊松内核给出。
In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the existence of Green's function by an application of Perron's method. After that, the Poisson kernel is constructed based on the Green's function. Several important properties of Green's functions and Poisson kernels are proved. Finally, we show that the solution of a fractional Laplace (Poisson) equation under a given condition must be unique and be given by our Green's function and Poisson kernel.
