*Published Paper*

**Inserted:** 6 feb 2009

**Last Updated:** 17 jul 2018

**Journal:** Comm. Partial Differential Equations

**Volume:** 35

**Pages:** 1-22

**Year:** 2010

**Abstract:**

Given a regular bounded domain $\Omega\subset\R{2m}$, we describe the
limiting behavior of sequences of solutions to the mean field equation of order
$2m$, $m\geq 1$, $$(-\Delta)^{m} u=\rho \frac{e^{{2mu}}{\int}_{\Omega}
e^{{2mu}dx}\quad\text{in}\Omega,$$} under the Dirichlet boundary condition and
the bound $0<\rho\leq C$. We emphasize the connection with the problem of
prescribing the $Q$-curvature.

**Keywords:**
Q-curvature, Concentration-compactness, Mean-field equation

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