
Journal of Convex Analysis 26 (2019), No. 1, 033047 Copyright Heldermann Verlag 2019 The CheegerNProblem in Terms of BVFunctions Marco Caroccia Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, U.S.A. caroccia.marco@gmail.com Samuel Littig Mathematical Institute, University of Cologne, Weyertal 8690, 50931 Cologne, Germany slittig@math.unikoeln.de We reformulate the CheegerNpartition problem as a minimization among a suitable class of BV functions. This allows us to obtain a new existence proof for the CheegerNproblem. Moreover, we derive some connections between the Cheeger2problem and the second eigenvalue of the 1Laplace operator. Keywords: CheegerNproblem, optimal partition, shape optimization, eigenvalue problem of the 1Laplace operator, second eigenvalue of the 1Laplace operator. MSC: 49Q20, 35P30, 49Q10 [ Fulltextpdf (133 KB)] for subscribers only. 