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Title The Gel'fand problem for the biharmonic operator

Name Olivier Goubet
Country France
Email olivier.goubet@u-picardie.fr
Co-Author(s) Louis Dupaigne, Marius Ghergu and Guillaume Warnault
Submit Time 2014-05-02 08:53:59
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
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 $N\leq 12$.