Critical polyharmonic systems and optimal partitions

We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in \begin{document}$ \mathbb{R}^N $\end{document} which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling parameters tend to \begin{document}$ -\infty $\end{document} . We show that the supports of the limiting profiles of their components are pairwise disjoint smooth domains and solve a nonlinear optimal partition problem of \begin{document}$ \mathbb R^N $\end{document} . We give a detailed description of the shape of these domains.