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 $\Phi$ 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 $\Phi$.

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

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• The Cheeger constant of a Jordan domain without necks
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Cited by in corpus (2)

• The Cheeger problem in abstract measure spaces
• Higher Cheeger ratios of features in Laplace-Beltrami eigenfunctions