Local behavior of positive solutions of higher order conformally invariant equations with a singular set

We study some properties of positive solutions to the higher order conformally invariant equation with a singular set $$\begin{aligned} (-\Delta )^m u = u^{\frac{n+2m}{n-2m}} ~~~~~~ \text {in} ~ \Omega \backslash \Lambda , \end{aligned}$$ where $$\Omega \subset {\mathbb {R}}^n$$ is an open domain, $$\Lambda $$ closed subset $${\mathbb $$1 \le m < n/2$$ and integer. first establish local estimate for solution near its when compact upper Minkowski dimension $$\overline{\text {dim}}_M(\Lambda ) \frac{n-2m}{2}$$ or smooth k-dimensional manifold $$k\le . Furthermore, we also show asymptotic symmetry supposing Finally, global result obtained whole space hyperplane