Fine properties of the subdifferential for a class of one-homogeneous functionals

Antonin Chambolle; Michael Goldman; Matteo Novaga

doi:10.1515/acv-2012-0025

Fine properties of the subdifferential for a class of one-homogeneous functionals

Antonin Chambolle
, Michael Goldman
, Matteo Novaga

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

Abstract

We collect some known results on the subdifferentials of a class of one-homogeneous functionals, which consist in anisotropic and nonhomogeneous variants of the total variation. It is known that the subdifferential at a point is the divergence of some "calibrating field". We establish new relationships between Lebesgue points of a calibrating field and regular points of the level surfaces of the corresponding calibrated function.

Original language	English
Pages (from-to)	31-42
Number of pages	12
Journal	Advances in Calculus of Variations
Volume	8
Issue number	1
DOIs	https://doi.org/10.1515/acv-2012-0025
Publication status	Published - 1 Jan 2015
Externally published	Yes

Keywords

Anisotropic energies
Calculus of variations
Calibrations
One-homogeneous functionals
Total variation

Access to Document

10.1515/acv-2012-0025

Cite this

@article{648cc8a3a75747fbbe64409e7b1b7185,

title = "Fine properties of the subdifferential for a class of one-homogeneous functionals",

abstract = "We collect some known results on the subdifferentials of a class of one-homogeneous functionals, which consist in anisotropic and nonhomogeneous variants of the total variation. It is known that the subdifferential at a point is the divergence of some {"}calibrating field{"}. We establish new relationships between Lebesgue points of a calibrating field and regular points of the level surfaces of the corresponding calibrated function.",

keywords = "Anisotropic energies, Calculus of variations, Calibrations, One-homogeneous functionals, Total variation",

author = "Antonin Chambolle and Michael Goldman and Matteo Novaga",

year = "2015",

month = jan,

day = "1",

doi = "10.1515/acv-2012-0025",

language = "English",

volume = "8",

pages = "31--42",

journal = "Advances in Calculus of Variations",

issn = "1864-8258",

number = "1",

}

TY - JOUR

T1 - Fine properties of the subdifferential for a class of one-homogeneous functionals

AU - Chambolle, Antonin

AU - Goldman, Michael

AU - Novaga, Matteo

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We collect some known results on the subdifferentials of a class of one-homogeneous functionals, which consist in anisotropic and nonhomogeneous variants of the total variation. It is known that the subdifferential at a point is the divergence of some "calibrating field". We establish new relationships between Lebesgue points of a calibrating field and regular points of the level surfaces of the corresponding calibrated function.

AB - We collect some known results on the subdifferentials of a class of one-homogeneous functionals, which consist in anisotropic and nonhomogeneous variants of the total variation. It is known that the subdifferential at a point is the divergence of some "calibrating field". We establish new relationships between Lebesgue points of a calibrating field and regular points of the level surfaces of the corresponding calibrated function.

KW - Anisotropic energies

KW - Calculus of variations

KW - Calibrations

KW - One-homogeneous functionals

KW - Total variation

U2 - 10.1515/acv-2012-0025

DO - 10.1515/acv-2012-0025

M3 - Article

AN - SCOPUS:84921000674

SN - 1864-8258

VL - 8

SP - 31

EP - 42

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

IS - 1

ER -

Fine properties of the subdifferential for a class of one-homogeneous functionals

Abstract

Keywords

Access to Document

Fingerprint

Cite this