Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains

Craig Cowan, Nassif Ghoussoub

We examine the fourth order problem ${\Delta }^{2}u=\lambda f(u)$ in $\Omega$ with $\Delta u=u=0$ on $\partial \Omega$, where $\lambda >0$ is a parameter, $\Omega$ is a bounded domain in $R^N$ and where $f$ is…