Minimizers for nonlocal perimeters of Minkowski type

Annalisa Cesaroni, Serena Dipierro, Matteo Novaga, Enrico Valdinoci

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Article number64
JournalCalculus of Variations and Partial Differential Equations
Volume57
Issue number2
DOIs
Publication statusPublished - 1 Apr 2018

Fingerprint

Perimeter
White noise
Minimizer
Rigidity
Concretes
Density Estimates
Isoperimetric Inequality
Irregularity
Preservation
Existence Results
Compactness
Interpolate
Perturbation
Series
Energy

Cite this

@article{b8f876fb3fc34d6c987241002db4f118,
title = "Minimizers for nonlocal perimeters of Minkowski type",
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, Poincar{\'e}–Wirtinger inequalities and density estimates. Furthermore, we provide the construction of planelike minimizers for this generalized perimeter under a small and periodic volume perturbation.",
keywords = "49N60, 49Q05",
author = "Annalisa Cesaroni and Serena Dipierro and Matteo Novaga and Enrico Valdinoci",
year = "2018",
month = "4",
day = "1",
doi = "10.1007/s00526-018-1335-9",
language = "English",
volume = "57",
journal = "Calculus of Variations and Partial Differential Equations",
issn = "0944-2669",
publisher = "Springer",
number = "2",

}

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 journalArticle

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 -