We study blow-up and quantization phenomena for a sequence of solutions \((u_k)\) to the prescribed Q-curvature problem

under natural assumptions on \(Q_k\). It is well-known that, up to a subsequence, either \((u_k)\) is bounded in a suitable norm, or there exists \(\beta _k\rightarrow \infty \) such that \( u_k=\beta _k(\varphi +o(1))\) in \(\Omega \setminus (S_1\cup S_\varphi )\) for some non-trivial non-positive n-harmonic function \(\varphi \) and for a finite set \(S_1\), where \(S_\varphi \) is the zero set of \(\varphi \). We prove quantization of the total curvature \(\int _{{\tilde{\Omega }}}Q_ke^{2nu_k}dx\) on the region \({\tilde{\Omega }}\Subset (\Omega \setminus S_\varphi )\).

我们研究给定Q曲率问题的一系列解\（（u_k）\）的爆炸和量化现象

在\（Q_k \）的自然假设下。众所周知，直到一个子序列，\（（u_k）\）都以合适的范数为界，或者存在\（\ beta _k \ rightarrow \ infty \）使得\（u_k = \ beta _k （\ varphi + O（1））\）在\（\欧米茄\ setminus（S_1 \杯S_ \ varphi）\）对于一些非平凡非正ñ K谐波函数\（\ varphi \）和对于有限集\（S_1 \） ，其中\（S_ \ varphi \）是零组\（\ varphi \） 。我们证明了全曲率的量化\（\ INT _ {{\波浪{\欧米茄}}} Q_ke ^ {} 2nu_k DX \）的区域\（{\波浪号{\ Omega}} \子集（\ Omega \ setminus S_ \ varphi）\）。