29

Existence of minimizing clusters

This chapter will be entirely devoted to the proof of the existence of minimizing clusters. Precisely, we shall prove the following theorem.

**Theorem 29.1** *For every* *and n* ≥ 2, *there exists a minimizer in the variational problem*

*If is a minimizer in (29.1), then is bounded, that is, for some R* > 0,

This proof ...

Start Free Trial

No credit card required