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

Ecole polytechnique
Max Planck Institute for Mathematics in the Sciences
Dipartimento di Matematica
University of Pisa

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

8 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	31-42
Nombre de pages	12
journal	Advances in Calculus of Variations
Volume	8
Numéro de publication	1
Les DOIs	https://doi.org/10.1515/acv-2012-0025
état	Publié - 1 janv. 2015
Modification externe	Oui

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10.1515/acv-2012-0025

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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",

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AU - Novaga, Matteo

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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

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AN - SCOPUS:84921000674

SN - 1864-8258

VL - 8

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EP - 42

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

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ER -

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

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