Calculus of Variations and Partial Differential Equations

, Volume 2, Issue 1, pp 17–27

On the structure of singular sets of convex functions

  • Giovanni Alberti

DOI: 10.1007/BF01234313

Cite this article as:
Alberti, G. Calc. Var (1994) 2: 17. doi:10.1007/BF01234313


Whenf is a convex function ofRh, andk is an integer with 0<k<h, then the setσk(f)=x:dim(∂f(x)k may be covered by countably many manifolds of dimensionh−k and classC2 except anh−k negligible subset.

Mathematics subject classification

26B25 Primary26B0549Q1552A20

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Giovanni Alberti
    • 1
  1. 1.Istituto di Matematiche ApplicatePisaIaly