论文标题
泊松问题涉及分数强的操作员和措施
Poisson Problems involving fractional Hardy operators and measures
论文作者
论文摘要
在本文中，我们研究了涉及分数强的操作员和测量源的泊松问题。与当地情况相比，操作员的非本地性质，奇特的效果和量度源之间的复杂相互作用会引起几种新的基本困难。为了克服这些困难，我们在加权分布意义上对双重操作员进行仔细的分析，并建立相关功能空间的良好特性，这又使我们能够在适当的框架中提出泊松问题。鉴于泊松问题及其双重问题之间的紧密联系，我们能够为泊松问题的理论建立各个方面，包括可溶性，先验估计，加托的不平等和规律性结果的变体。
In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source induces several new fundamental difficulties in comparison with the local case. To overcome these difficulties, we perform a careful analysis of the dual operator in the weighted distributional sense and establish fine properties of the associated function spaces, which in turn allow us to formulate the Poisson problem in an appropriate framework. In light of the close connection between the Poisson problem and its dual problem, we are able to establish various aspects of the theory for the Poisson problem including the solvability, a priori estimates, variants of Kato's inequality and regularity results.
