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(k)e(2muk) on open domains of R(2m). Under natural integral assumptions we show that when blow-up occurs, up to a subsequence lim(k ->infinity)integral(Omega 0) V(k)e(2muk)dx = L Lambda(1), where Omega(0) subset of Omega is open and contains the blow-up points, L is an element of 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(k) is positive.