Calculus of Variations and Geometric Measure Theory

A. Cesaroni - S. Dipierro - M. Novaga - E. Valdinoci

Minimizers for nonlocal perimeters of Minkowski type

created by novaga on 11 Apr 2017
modified on 16 Mar 2018


Published Paper

Inserted: 11 apr 2017
Last Updated: 16 mar 2018

Journal: Calc. Var. Partial Differential Equations
Volume: 57
Number: 2
Pages: Art. 64, 40 pages
Year: 2018


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, com- pactness results, isoperimetric inequalities, Poincare'-Wirtinger inequalities and density estimates. Furthermore, we provide the construction of planelike minimizers for this generalized perimeter under a small and periodic volume perturbation.