论文标题
布雷兹·尼伦贝格问题的多吹炸分析在三个方面
Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions
论文作者
论文摘要
对于平滑界面域$ω\ subset \ mathbb r^3 $和光滑函数$ a $和$ v $，我们考虑了一系列阳性解决方案的渐近行为$u_ε$ to $u_ε$ to $-ΔU_ε+（a+εv）u_i_ε=u_ε=u_ε=u_ε^5 $ on $ po $ ocy of $ω$ a $ω$ a dirichlet dirichlet dirichlet tirichlet tirichlet up dirichlet up diricheled up up up y $ to $ to $ to $。我们得出了尖锐的爆炸率，并表征了多个爆炸的一般情况下的浓度点的位置，从而在尺寸$ n = 3 $的Brezis-Peletier猜想的框架内获得了爆炸现象的完整图片。
For a smooth bounded domain $Ω\subset \mathbb R^3$ and smooth functions $a$ and $V$, we consider the asymptotic behavior of a sequence of positive solutions $u_ε$ to $-Δu_ε+ (a+εV) u_ε= u_ε^5$ on $Ω$ with zero Dirichlet boundary conditions, which blow up as $ε\to 0$. We derive the sharp blow-up rate and characterize the location of concentration points in the general case of multiple blow-up, thereby obtaining a complete picture of blow-up phenomena in the framework of the Brezis-Peletier conjecture in dimension $N=3$.
