On the higher Cheeger problem
Résumé
We develop the notion of higher Cheeger constants for a measurable set RN. By the kth Cheeger constant we mean the value where the infimum is taken over all k-tuples of mutually disjoint subsets of , and h1(Ei) is the classical Cheeger constant of Ei. We prove the existence of minimizers satisfying additional adjustment' conditions and study their properties. A relation between hk() and spectral minimal k-partitions of associated with the first eigenvalues of the p-Laplacian under homogeneous Dirichlet boundary conditions is stated. The results are applied to determine the second Cheeger constant of radially symmetric planar domains.