The fractional Cheeger problem

  • Lorenzo Brasco

    Aix-Marseille Université, France
  • Erik Lindgren

    KTH Royal Institute of Technology, Stockholm, Sweden
  • Enea Parini

    Aix-Marseille Université, France


Given an open and bounded set ΩRN\Omega\subset\mathbb{R}^N, we consider the problem of minimizing the ratio between the ss-perimeter and the NN-dimensional Lebesgue measure among subsets of Ω\Omega. This is the nonlocal version of the well-known Cheeger problem. We prove various properties of optimal sets for this problem, as well as some equivalent formulations. In addition, the limiting behaviour of some nonlinear and nonlocal eigenvalue problems is investigated, in relation with this optimization problem. The presentation is as self-contained as possible.

Cite this article

Lorenzo Brasco, Erik Lindgren, Enea Parini, The fractional Cheeger problem. Interfaces Free Bound. 16 (2014), no. 3, pp. 419–458

DOI 10.4171/IFB/325