Minimizers for nonlocal perimeters of Minkowski type

  • Annalisa Cesaroni
  • Serena Dipierro
  • Matteo Novaga
  • Enrico Valdinoci


We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This nonlocal functionals arise in concrete applications, since the nonlocal character of the problems and the different behaviors of the energy at different scales allow the preservation of details and irregularities of the image in the process of removing white noises, thus improving the quality of the image without losing relevant features. In this paper, we provide a series of results concerning existence, rigidity and classification of minimizers, compactness results, isoperimetric inequalities, Poincaré–Wirtinger inequalities and density estimates. Furthermore, we provide the construction of planelike minimizers for this generalized perimeter under a small and periodic volume perturbation.

Mathematics Subject Classification

49Q05 49N60 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Annalisa Cesaroni
    • 1
  • Serena Dipierro
    • 2
  • Matteo Novaga
    • 3
  • Enrico Valdinoci
    • 2
    • 4
    • 5
  1. 1.Dipartimento di Scienze StatisticheUniversità di PadovaPaduaItaly
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanItaly
  3. 3.Dipartimento di MatematicaUniversità di PisaPisaItaly
  4. 4.School of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia
  5. 5.IMATI-CNRPaviaItaly

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