Title: On the higher Cheeger problem
Authors: Bobkov, Vladimír
Parini, Enea
Issue Date: 2018
Publisher: London Mathematical Society
Oxford University Press
Document type: článek
URI: 2-s2.0-85044475007
ISSN: 0024-6107
Keywords in different language: Cheeger problem;higher Cheeger problem;optimal partitions;p-Laplacian.
Abstract in different language: We develop the notion of higher Cheeger constants for a measurable set $\Omega \subset \mathbb{R}^N$. By the $k$-th Cheeger constant we mean the value \[h_k(\Omega) = \inf \max \{h_1(E_1), \dots, h_1(E_k)\},\] where the infimum is taken over all $k$-tuples of mutually disjoint subsets of $\Omega$, and $h_1(E_i)$ is the classical Cheeger constant of $E_i$. We prove the existence of minimizers satisfying additional ``adjustment'' conditions and study their properties. A relation between $h_k(\Omega)$ and spectral minimal $k$-partitions of $\Omega$ 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 some planar domains.
Rights: Plný text není přístupný.
© Wiley - London Mathematical Society - Oxford University Press
Appears in Collections:Články / Articles (KMA)

Please use this identifier to cite or link to this item: http://hdl.handle.net/11025/30448

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