On the $N$-Cheeger problem for component-wise increasing norms

Abstract

We study Cheeger and $p$-eigenvalue partition problems depending on a given evaluation function $\hat{I}¦$ for $p\in [1,\infty )$. We prove existence and regularity of minima, relations among the problems, convergence, and stability with respect to $p$ and to $\hat{I}¦$.

33 pages. Due to a miscommunication, we received one report after publication. This version incorporates the report's feedback and corrects the statement of Lemma 4.17 by adding a missing hypothesis