# Asymptotics and quantization for a mean-field equation of higher order

created by martinazz on 06 Feb 2009
modified on 17 Jul 2018

[BibTeX]

Published Paper

Inserted: 6 feb 2009
Last Updated: 17 jul 2018

Journal: Comm. Partial Differential Equations
Volume: 35
Pages: 1-22
Year: 2010

ArXiv: 0904.3290 PDF

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.