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Proceedings of the American Mathematical Society

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Differentiability of the metric projection in finite-dimensional Euclidean space


Author: Edgar Asplund
Journal: Proc. Amer. Math. Soc. 38 (1973), 218-219
DOI: https://doi.org/10.1090/S0002-9939-1973-0310150-X
MathSciNet review: 0310150
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Abstract | References | Additional Information

Abstract: The metric projection on a closed subset of a finite-dimensional Euclidean space is almost everywhere differentiable.


References [Enhancements On Off] (What's this?)

  • [1] A. D. Alexandrov, Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it, Leningrad State Univ. Ann. Math. Ser. 6 (1939), 3-35. MR 2, 155. MR 0003051 (2:155a)
  • [2] E. Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31-47. MR 37 #6754. MR 0231199 (37:6754)
  • [3] J. B. Kruskal, Two convex counterexamples: A discontinuous envelope function and a nondifferentiable nearest-point mapping, Proc. Amer. Math. Soc. 23 (1969), 697-703. MR 41 #4385. MR 0259752 (41:4385)
  • [4] Ju. G. Rešetnjak, Generalized derivatives and differentiability almost everywhere, Mat. Sb. 75 (117) (1968), 323-334 = Math. USSR Sb. 4 (1968), 293-302. MR 37 #754. MR 0225159 (37:754)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310150-X
Keywords: Metric projection, differentiability
Article copyright: © Copyright 1973 American Mathematical Society

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