论文标题
分数拉普拉斯（Laplacian
Uniqueness and some related estimates for Dirichlet problem with fractional Laplacian
论文作者
论文摘要
对于分数拉普拉斯方程，令人惊讶的观察结果是基本的dirichlet类型问题的非唯一性。在本文中，建立了分数拉普拉斯方程的鲜明独特条件。我们得出了分数拉普拉斯运营商的$ l^p $ estimate，以更好地理解这种现象。几个加权分数Sobolev空间自然出现。然后，我们建立这些空间之间的嵌入关系。这些存在的唯一性条件和我们在此处引入的空间与分数拉普拉斯（Laplacian）本质上相关。这些是分数拉普拉斯方程的基本属性，在研究相关问题的研究中很有用。
For the fractional Laplace equation, a surprising observation is the non-uniqueness for the basic Dirichlet type problems. In this paper, a somewhat sharp uniqueness condition for the fractional Laplace equation is established. We derive the $L^p$-estimate for fractional Laplacian operators to better understand this phenomena. Several weighted fractional Sobolev spaces appear naturally. We then establish the embedding relations between these spaces. These existence-uniqueness conditions and the spaces we introduce here are intrinsically related to the fractional Laplacian. These are basic properties to the fractional Laplace equations and can be useful in the study of related problems.
