论文标题
在涉及laplacian的平方根上的分数nirenberg问题上
On a Fractional Nirenberg problem involving the square root of the Laplacian on $\mathbb{S}^{3}$
论文作者
论文摘要
在本文中，我们致力于建立$ n = 3，$ $σ= 1/2的分数Nirenberg问题的紧凑性和存在结果，当开处方$σ$ curvature函数满足$（n-2σ）$ - 平坦度附近的平坦度条件时。紧凑性结果是新的和最佳的。此外，我们获得了所有解决方案的学位公式。从我们的结果来看，我们可以知道发生爆炸的地方。此外，对于任何有限的不同点，都可以构建精确地炸毁这些点的解决方案的顺序。我们将li的结果扩展在\ cite [cpam，1996] {lyy}中，从局部问题到非局部情况。
In this paper, we are devoted to establishing the compactness and existence results of the solutions to the fractional Nirenberg problem for $n=3,$ $σ=1/2,$ when the prescribing $σ$-curvature function satisfies the $(n-2σ)$-flatness condition near its critical points. The compactness results are new and optimal. In addition, we obtain a degree-counting formula of all solutions. From our results, we can know where blow up occur. Moreover, for any finite distinct points, the sequence of solutions that blow up precisely at these points can be constructed. We extend the results of Li in \cite[CPAM, 1996]{LYY} from the local problem to nonlocal cases.
