Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition

Details Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition

2007-06-05

arxiv.org/abs/0706.0615v3

Mathematics

Analysis of PDEs

Updated version. To appear in "Indiana University Math. Journal"

Scientific paper

We consider asymptotic behavior of the following fourth order equation \[
\Delta^2 u= \rho \frac{e^{u}}{\int_\Om e^{u} dx} {in} \Om, u= \partial_\nu u=0
{on} \partial \Omega \] where $\Om$ is a smooth oriented bounded domain in
$\R^4$. Assuming that $0<\rho \leq C$, we completely characterize the
asymptotic behavior of the unbounded solutions.

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