Louis Dupaigne, Marius Ghergu and Guillaume Warnault
Submit Time
2014-05-02 08:53:59
Session
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
Contents
We study stable solutions of the equation $\Delta^2 u = e^{u}$ in bounded domains $\Omega \subset \mathbb{R}^N$. We prove that the extremal solutions are smooth if $N\leq 12$.