Abstract
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.
| Original language | English |
|---|---|
| Article number | 64 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 57 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2018 |
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Minimizers for nonlocal perimeters of Minkowski type. / Cesaroni, Annalisa; Dipierro, Serena; Novaga, Matteo; Valdinoci, Enrico.
In: Calculus of Variations and Partial Differential Equations, Vol. 57, No. 2, 64, 01.04.2018.Research output: Contribution to journal › Article
TY - JOUR
T1 - Minimizers for nonlocal perimeters of Minkowski type
AU - Cesaroni, Annalisa
AU - Dipierro, Serena
AU - Novaga, Matteo
AU - Valdinoci, Enrico
PY - 2018/4/1
Y1 - 2018/4/1
N2 - 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.
AB - 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.
KW - 49N60
KW - 49Q05
UR - http://www.scopus.com/inward/record.url?scp=85044186747&partnerID=8YFLogxK
U2 - 10.1007/s00526-018-1335-9
DO - 10.1007/s00526-018-1335-9
M3 - Article
VL - 57
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 2
M1 - 64
ER -