A priori bounds for energy-bounded solutions of critical polyharmonic equations

We investigate critical polyharmonic equations of the type: $$ Lu = |u|^{2^\sharp-2} u \quad \text{ in } Ω$$ with Dirichlet boundary conditions, in a smooth bounded domain $Ω$ of $\mathbb{R}^n$. Here $L$ is an elliptic differential operator of integer order $2 \le 2k < n$ whose leading order term is