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Journal of Convex Analysis 26 (2019), No. 1, 033--047
Copyright Heldermann Verlag 2019

The Cheeger-N-Problem in Terms of BV-Functions

Marco Caroccia
Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, U.S.A.

Samuel Littig
Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany

We reformulate the Cheeger-N-partition problem as a minimization among a suitable class of BV functions. This allows us to obtain a new existence proof for the Cheeger-N-problem. Moreover, we derive some connections between the Cheeger-2-problem and the second eigenvalue of the 1-Laplace operator.

Keywords: Cheeger-N-problem, optimal partition, shape optimization, eigenvalue problem of the 1-Laplace operator, second eigenvalue of the 1-Laplace operator.

MSC: 49Q20, 35P30, 49Q10

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