Nonsmooth analysis on smooth manifolds

Ledyaev, Yu.; Zhu, Qiji

doi:10.1090/S0002-9947-07-04075-5

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.

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