In this manuscript, we appeal to Potential Theory to provide a sufficient condition for existence of distributional solutions to fractional elliptic problems with non-linear first-order terms and measure data ω:

under suitable assumptions on q and ω. Roughly speaking, the condition for existence states that if the measure data is locally controlled by the Riesz fractional capacity, then there is a global solution for the Problem (1). We also show that if a positive solution exists, necessarily the measure ω will be absolutely continuous with respect to the associated Riesz capacity, which gives a partial reciprocal of the main result of this work. Finally, estimates of u in terms of ω are also given in different function spaces.

在这个手稿中，我们呼吁潜在的理论，为与非线性的一阶项和测量数据分数椭圆分布问题解的存在性提供了充分条件ω：

在q和ω的适当假设下。粗略地说，存在的条件是，如果度量数据由Riesz分数容量局部控制，则存在针对问题（1）的全局解决方案。我们还表明，如果存在正解，则度量ω相对于相关的Riesz容量必定是绝对连续的，这部分代表了这项工作的主要结果。最后，估计ü来讲ω在不同的功能空间也给出。