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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory by Francesco Maggi

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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 images and n ≥ 2, there exists a minimizer in the variational problem

images

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

This proof ...

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