Nonsmooth analysis on smooth manifolds
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- by Yu. S. Ledyaev and Qiji J. Zhu PDF
- Trans. Amer. Math. Soc. 359 (2007), 3687-3732 Request permission
Abstract:
We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function. A subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems, nonclassical problems of calculus of variations, and generalized solutions of first-order partial differential equations on manifolds. We also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions.References
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Additional Information
- Yu. S. Ledyaev
- Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008 – and – Steklov Institute of Mathematics, Moscow 117966, Russia
- Email: ledyaev@wmich.edu
- Qiji J. Zhu
- Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008
- Email: zhu@wmich.edu
- Received by editor(s): June 20, 2003
- Received by editor(s) in revised form: May 5, 2005
- Published electronically: February 23, 2007
- Additional Notes: The first author was supported in part by NSF grant #0102496 and by the Russian Fund for Fundamental Research Grant # 02-01-00769.
The second author was supported in part by NSF grants #9704203, #0102496 and by the Faculty Research and Creative Activities Support Fund at Western Michigan University. - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 3687-3732
- MSC (2000): Primary 93D05, 93D20, 34D20
- DOI: https://doi.org/10.1090/S0002-9947-07-04075-5
- MathSciNet review: 2302512