论文标题
高维brezis-nirenberg问题中的精细多吹分析
Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem
论文作者
论文摘要
对于有界的集合$ω\ subset \ mathbb r^n $和c^1（\overlineΩ）$中的扰动$ v \，我们分析了阳性解决方案爆炸序列的浓度行为\ [-Δu_iM+εv= n（n-2）从勃雷氏症的意义上讲是非批判性的 - 尼伦贝格问题。 对于多个浓度点的一般情况，我们证明浓度点是孤立的，并将这些点的向量表征为$-δ$ of $ω$的绿色函数的合适函数的临界点。此外，我们给出浓度速度的领先顺序表达。本文由作者（Arxiv：2208.12337）的最新论文$ n = 3 $，提供了Brezis-Nirenberg框架中爆炸现象的完整图片。
For a bounded set $Ω\subset \mathbb R^N$ and a perturbation $V \in C^1(\overlineΩ)$, we analyze the concentration behavior of a blow-up sequence of positive solutions to \[ -Δu_ε+ εV = N(N-2) u_ε^\frac{N+2}{N-2} \] for dimensions $N \geq 4$, which are non-critical in the sense of the Brezis--Nirenberg problem. For the general case of multiple concentration points, we prove that concentration points are isolated and characterize the vector of these points as a critical point of a suitable function derived from the Green's function of $-Δ$ on $Ω$. Moreover, we give the leading order expression of the concentration speed. This paper, with a recent one by the authors (arXiv:2208.12337) in dimension $N = 3$, gives a complete picture of blow-up phenomena in the Brezis-Nirenberg framework.
