Minimizers of the p-oscillation functional

Annalisa Cesaroni; Serena Dipierro; Matteo Novaga; Enrico Valdinoci

doi:10.3934/dcds.2019231

Minimizers of the p-oscillation functional

Annalisa Cesaroni, Serena Dipierro, Matteo Novaga, Enrico Valdinoci

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for p = 1 and of the p-Dirichlet functionals for p > 1. We introduce the notion of minimizers and prove existence of solutions to the Dirichlet problem. Finally we provide a description of Class A minimizers (i.e. minimizers under compact perturbations) in dimension 1.

Original language	English
Pages (from-to)	6785-6799
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	39
Issue number	12
DOIs	https://doi.org/10.3934/dcds.2019231
Publication status	Published - Jun 2019

Access to Document

10.3934/dcds.2019231

https://arxiv.org/abs/1803.01371

Cite this

@article{138412596522400f8dab7c61af9cc013,

title = "Minimizers of the p-oscillation functional",

abstract = "We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for p = 1 and of the p-Dirichlet functionals for p > 1. We introduce the notion of minimizers and prove existence of solutions to the Dirichlet problem. Finally we provide a description of Class A minimizers (i.e. minimizers under compact perturbations) in dimension 1.",

keywords = "Discrete total variation functional, Minimizers, Minkowski content, One-dimensional solutions, P-oscillation functional",

author = "Annalisa Cesaroni and Serena Dipierro and Matteo Novaga and Enrico Valdinoci",

year = "2019",

month = jun,

doi = "10.3934/dcds.2019231",

language = "English",

volume = "39",

pages = "6785--6799",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "12",

}

TY - JOUR

T1 - Minimizers of the p-oscillation functional

AU - Cesaroni, Annalisa

AU - Dipierro, Serena

AU - Novaga, Matteo

AU - Valdinoci, Enrico

PY - 2019/6

Y1 - 2019/6

N2 - We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for p = 1 and of the p-Dirichlet functionals for p > 1. We introduce the notion of minimizers and prove existence of solutions to the Dirichlet problem. Finally we provide a description of Class A minimizers (i.e. minimizers under compact perturbations) in dimension 1.

AB - We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for p = 1 and of the p-Dirichlet functionals for p > 1. We introduce the notion of minimizers and prove existence of solutions to the Dirichlet problem. Finally we provide a description of Class A minimizers (i.e. minimizers under compact perturbations) in dimension 1.

KW - Discrete total variation functional

KW - Minimizers

KW - Minkowski content

KW - One-dimensional solutions

KW - P-oscillation functional

UR - http://www.scopus.com/inward/record.url?scp=85072922848&partnerID=8YFLogxK

U2 - 10.3934/dcds.2019231

DO - 10.3934/dcds.2019231

M3 - Article

AN - SCOPUS:85072922848

SN - 1078-0947

VL - 39

SP - 6785

EP - 6799

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 12

ER -

Minimizers of the p-oscillation functional

Abstract

Access to Document

Other files and links

Fingerprint

Nonlocal Equations at Work

Cite this

Minimizers of the p-oscillation functional

Abstract

Access to Document

Other files and links

Fingerprint

Projects

Nonlocal Equations at Work

Cite this