Nonlocal Cheeger and Calibrable Sets

  • José M. Mazón
  • Julio Daniel Rossi
  • J. Julián Toledo
Part of the Frontiers in Mathematics book series (FM)


Given a non-null, measurable and bounded set \(\Omega \subset \mathbb {R}^N\), we define its J-Cheeger constant


  1. 4.
    F. Alter, V. Caselles, Uniqueness of the Cheeger set of a convex body. Nonlinear Anal. Theory Methods Appl. 70, 32–44 (2009)MathSciNetCrossRefGoogle Scholar
  2. 5.
    F. Alter, V. Caselles, A. Chambolle, A characterization of convex calibrable sets in \(\mathbb {R}^N\). Math. Ann. 332, 329–366 (2005)MathSciNetCrossRefGoogle Scholar
  3. 12.
    F. Andreu-Vaillo, J.M. Mazón, J.D. Rossi, J. Toledo, Nonlocal Diffusion Problems. Mathematical Surveys and Monographs, vol. 165 (American Mathematical Society, Providence, 2010)Google Scholar
  4. 18.
    L. Brasco, E. Lindgren, E. Parini, The fractional Cheeger problem. Interfaces Free Bound. 16, 419–458 (2014)MathSciNetCrossRefGoogle Scholar
  5. 21.
    H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext/Springer, Heidelberg, 2011)zbMATHGoogle Scholar
  6. 40.
    I. Ekeland, Convexity Methods in Hamiltonian Mechanics (Springer, Berlin, 1990)CrossRefGoogle Scholar
  7. 49.
    V. Fridman, B. Kawohl, Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant. Comment. Math. Univ. Carol. 44, 659–667 (2003)MathSciNetzbMATHGoogle Scholar
  8. 52.
    D. Grieser, The first eigenvalue of the Laplacian, isoperimetric constants, and the max ow min cut theorem. Arch. Math. (Basel) 87, 75–85 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • José M. Mazón
    • 1
  • Julio Daniel Rossi
    • 2
  • J. Julián Toledo
    • 3
  1. 1.Departamento de Análisis MatemáticoUniversitat de ValènciaValenciaSpain
  2. 2.Departamento de MatemáticasUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.Departamento de Análisis MatemáticoUniversitat de ValènciaValènciaSpain

Personalised recommendations