论文标题
CKN操作员的椭圆问题的定性特性
Qualitative properties for elliptic problems with CKN operators
论文作者
论文摘要
本文的目的是研究操作员的基本属性 $$\mathcal{L}_{μ_1,μ_2} u=-Δ+\frac{μ_1 }{|x|^2}x\cdot\nabla +\frac{μ_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where $μ_1,μ_2$是免费参数。该操作员源于关键的Caffarelli-Kohn-Nirenberg不平等。我们通过使用与该操作员的Liouville定理一起分析了与该操作员的Liouville定理，并通过使用在有界域$ω\ subset \ subset \ subset \ subset \ mathbb {r}^n $ n $（$ n $ n \ geq 2 $）中的孤立单数解决方案进行分类。
The purpose of this paper is to study basic property of the operator $$\mathcal{L}_{μ_1,μ_2} u=-Δ+\frac{μ_1 }{|x|^2}x\cdot\nabla +\frac{μ_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where $μ_1,μ_2$ are free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of isolated singular solutions of the related Poisson problem in a bounded domain $Ω\subset \mathbb{R}^N$ ($N \geq 2$) containing the origin.
