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Fine properties of the subdifferential for a class of one-homogeneous functionals
-
Antonin Chambolle
,
Michael Goldman
Published/Copyright:
February 7, 2014
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: One-homogeneous functionals; calibrations; anisotropic energies; total variation; calculus of variations
Funding source: von Humboldt PostDoc fellowship
Funding source: ANR
Award Identifier / Grant number: ANR-12-BS01-0014-01 GEOMETRYA
Received: 2012-10-30
Revised: 2013-12-15
Accepted: 2013-12-18
Published Online: 2014-2-7
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Bi-Sobolev homeomorphism with zero minors almost everywhere
- Fine properties of the subdifferential for a class of one-homogeneous functionals
- Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
- Regularity of minimizers of the area functional in metric spaces
- On the relaxation of variational integrals in metric Sobolev spaces
Keywords for this article
One-homogeneous functionals;
calibrations;
anisotropic energies;
total variation;
calculus of variations
Articles in the same Issue
- Frontmatter
- Bi-Sobolev homeomorphism with zero minors almost everywhere
- Fine properties of the subdifferential for a class of one-homogeneous functionals
- Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
- Regularity of minimizers of the area functional in metric spaces
- On the relaxation of variational integrals in metric Sobolev spaces
