• Media type: E-Article
  • Title: Nonsmooth Analysis on Smooth Manifolds
  • Contributor: Ledyaev, Yu. S.; Zhu, Qiji J.
  • Published: American Mathematical Society, 2007
  • Published in: Transactions of the American Mathematical Society, 359 (2007) 8, Seite 3687-3732
  • Language: English
  • ISSN: 0002-9947
  • Origination:
  • Footnote:
  • Description: 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.
  • Access State: Open Access