Title: On the higher Cheeger problem Authors: Bobkov, VladimírParini, Enea Issue Date: 2018 Publisher: London Mathematical SocietyWileyOxford University Press Document type: článekarticle URI: 2-s2.0-85044475007http://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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