On the structure of singular sets of convex functions

  • Giovanni Alberti
Article

Abstract

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 Primary 26B05 49Q15 52A20 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

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

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