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

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

8 Citations (Scopus)

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

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10.1515/acv-2012-0025

Cite this

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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

M3 - Article

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VL - 8

SP - 31

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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

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