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Transactions of the American Mathematical Society

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Limiting subhessians, limiting subjets
and their calculus


Authors: Alexander D. Ioffe and Jean-Paul Penot
Journal: Trans. Amer. Math. Soc. 349 (1997), 789-807
MSC (1991): Primary 28A15, 46G05; Secondary 26A24, 26A27
DOI: https://doi.org/10.1090/S0002-9947-97-01726-1
MathSciNet review: 1373640
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Abstract: We study calculus rules for limiting subjets of order two. These subjets are obtained as limits of sequences of subjets, a subjet of a function $f$ at some point $x$ being the Taylor expansion of a twice differentiable function which minorizes $f$ and coincides with $f$ at $x$. These calculus rules are deduced from approximate (or fuzzy) calculus rules for subjets of order two. In turn, these rules are consequences of delicate results of Crandall-Ishii-Lions. We point out the similarities and the differences with the case of first order limiting subdifferentials.


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Additional Information

Alexander D. Ioffe
Affiliation: Department of Mathematics, Technion, 32000 Haifa, Israel

Jean-Paul Penot
Affiliation: Départment de Mathématiques, CNRS URA 1204, Faculté des Sciences, Av. de l’Université, 64000 Pau, France
Email: jean-paul.penot@univ.pau-fr

DOI: https://doi.org/10.1090/S0002-9947-97-01726-1
Received by editor(s): August 3, 1994
Received by editor(s) in revised form: September 5, 1995
Additional Notes: The first author’s research was supported in part by the U.S.-Israel Binational Science Foundation, under grant no. 90-00455
Article copyright: © Copyright 1997 American Mathematical Society

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