A priori bounds and a Liouville theorem on a half-space for higher order elliptic Dirichlet problems

Wolfgang Reichel, Tobias Weth

We consider the $2m$-th order elliptic boundary value problem $Lu=f(x,u)$ on a bounded smooth domain $\Omega$ in $R^N$ with Dirichlet boundary conditions. The operator $L$ is a uniforml…