Title: | On the higher Cheeger problem |
Authors: | Bobkov, Vladimír Parini, Enea |
Issue Date: | 2018 |
Publisher: | London Mathematical Society Wiley Oxford University Press |
Document type: | článek article |
URI: | 2-s2.0-85044475007 http://hdl.handle.net/11025/30448 |
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) OBD |
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