Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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 86-90, 50931 Cologne, Germany

slittig@math.uni-koeln.de

Keywords

  • Cheeger-N-problem
  • optimal partition
  • shape optimization
  • eigenvalue problem of the 1-Laplace operator
  • second eigenvalue of the 1-Laplace operator

Mathematics Subject Classification

49Q20, 35P30, 49Q10

Suggested citation

M. Caroccia, S. Littig. “The Cheeger-N-Problem in Terms of BV-Functions.” Journal of Convex Analysis 26 (2019), No. 1, 33–47.

Copyright Banach Press 2019