We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension of the celebrated theorem of Caffarelli-Gidas-Spruck for the second order Yamabe equation with isolated singularities to higher order equations. Our approach uses blow up analysis for local integral equations, and is unified for all critical elliptic equations of order smaller than the dimension. We also prove the existence of Fowler solutions to the global equations, and establish a sup ⁎ inf type Harnack inequality of Schoen for integral equations.

我们证明了具有孤立奇点的有界域中高阶共形不变方程解的急剧膨胀率，并显示了奇点附近解的渐近径向对称性。这是具有孤立奇点的二阶 Yamabe 方程的著名 Caffarelli-Gidas-Spruck 定理到更高阶方程的扩展。我们的方法对局部积分方程使用爆破分析，并对所有阶次小于维数的临界椭圆方程进行统一。我们还证明了全局方程的 Fowler 解的存在性，并建立了积分方程的 Schoen 的 sup ⁎ inf 型 Harnack 不等式。