论文标题
在刺穿球中，用于共同不变的第四阶系统的单数解决方案的渐近方法
Asymptotics for singular solutions to conformally invariant fourth order systems in the punctured ball
论文作者
论文摘要
我们研究了奇异解决方案的渐近行为，以推广$ q $ curvature方程的关键第四阶系统。我们的主要结果扩展到了强耦合系统的情况，即由于[L. A. Caffarelli，B。Gidas和J. Spruck，Comm。纯应用。数学。 （1989）]和[N。 Korevaar，R。Mazzeo，F。Pacard和R. Schoen，发明。数学，（1999）]。在技术层面上，我们使用涉及的光谱分析来研究系统在系统的线性化围绕爆破极限解决方案的线性化中的雅各比田的生长特性。此外，我们获得了对原点附近奇异溶液的衰减速率的先验估计。因此，我们证明，足够接近孤立的奇异性解决方案的行为就像所谓的emden-foller溶液。我们的主要定理积极回答了[R. L. Frank和T.König，肛门。 PDE（2019）]关于刺穿球中标量溶液的隔离奇点的局部行为。
We study the asymptotic behavior for singular solutions to a critical fourth order system generalizing the constant $Q$-curvature equation. Our main result extends to the case of strongly coupled systems, the celebrated asymptotic classification due to [L. A. Caffarelli, B. Gidas and J. Spruck, Comm. Pure Appl. Math. (1989)] and [N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen, Invent. Math., (1999)]. On the technical level, we use an involved spectral analysis to study the Jacobi fields' growth properties in the kernel of the linearization of our system around a blow-up limit solution. Besides, we obtain sharp a priori estimates for the decay rate of singular solutions near the origin. Consequently, we prove that sufficiently close to the isolated singularity solutions behave like the so-called Emden--Fowler solution. Our main theorem positively answers a question posed by [R. L. Frank and T. König, Anal. PDE (2019)] concerning the local behavior close to the isolated singularity for scalar solutions in the punctured ball.
