Reconstruction of the Clarke Subdifferential by the Lasry–Lions Regularizations

We prove that the Clarke subdifferential of a locally Lipschitz function with a growth condition, defined on a Hilbert space, can be represented by the derivatives of its Lasry–Lions regularizations. We complete a result of J. Benoist, showing a similar representation for the Clarke subdifferential...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 248; no. 2; pp. 415 - 428
Main Authors Georgiev, Pando Gr, Zlateva, Nadia P.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.08.2000
Elsevier
Subjects
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematics
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Reconstruction
Lasry Lions regularization
Moreau Yosid regularization
Subdifferential
Clark subdifferential
Lipschitz function
Hilbert space
Regularization
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Summary:We prove that the Clarke subdifferential of a locally Lipschitz function with a growth condition, defined on a Hilbert space, can be represented by the derivatives of its Lasry–Lions regularizations. We complete a result of J. Benoist, showing a similar representation for the Clarke subdifferential of a Lipschitz function in an arbitrary Banach space, by the Clarke subdifferentials of its Lasry–Lions regularizations.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2000.6916