Calculus of Variations and Partial Differential Equations

, Volume 2, Issue 1, pp 17-27

First online:

On the structure of singular sets of convex functions

  • Giovanni AlbertiAffiliated withIstituto di Matematiche Applicate

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Whenf is a convex function ofR h, andk is an integer with 0<k<h, then the setσ k (f)=x:dim(∂f(x)k may be covered by countably many manifolds of dimensionh−k and classC 2 except an h−k negligible subset.

Mathematics subject classification

26B25 Primary 26B05 49Q15 52A20