Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization for the prescribed Q-curvature equation on open domains   We discuss compactness, blow-up and quantization phenomena for the prescribed
$Q$-curvature equation $(-\Delta)^m u_k=V_ke^{2mu_k}$ on open domains of
$\R{2m}$. Under natural integral assumptions we show that when blow-up occurs,
up to a subsequence $$\lim_{k\to \infty}\int_{\Omega_0}
V_ke^{2mu_k}dx=L\Lambda_1,$$ where $\Omega_0\subset\subset\Omega$ is open and
contains the blow-up points, $L\in\mathbb{N}$ and
$\Lambda_1:=(2m-1)!\vol(S^{2m})$ is the total $Q$-curvature of the round sphere
$S^{2m}$. Moreover, under suitable assumptions, the blow-up points are
isolated. We do not assume that $V$ is positive.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn