An introduction to the Cheeger problem,. (English) Zbl 1399.49023
Summary: Given a bounded domain \(\Omega\subset\mathbb{R}^n\) with Lipschitz boundary, the Cheeger problem consists of finding a subset \(E\) of \(\Omega\) such that its ratio perimeter/volume is minimal among all subsets of \(\Omega\). This article is a collection of some known results about the Cheeger problem which are spread in many classical and new papers.
MSC:
49Q20 | Variational problems in a geometric measure-theoretic setting |
49-02 | Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control |