Calculus of Variations and Geometric Measure Theory

G. Saracco - G. Stefani

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

created by stefani on 29 Jan 2024
modified by saracco on 26 Jun 2024


Published Paper

Inserted: 29 jan 2024
Last Updated: 26 jun 2024

Journal: J. Math. Pures Appl. (9)
Year: 2024
Doi: 10.1016/j.matpur.2024.06.008

ArXiv: 2401.16041 PDF


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 $\Phi$.

Keywords: Cheeger constant, partition, isoperimetric, spectral, Dirichlet eigenvalue