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On the structure of singular sets of convex functions

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Abstract

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 anℋ h−k negligible subset.

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  1. Istituto di Matematiche Applicate, Via Bonanno 25/B, I-56100, Pisa, Ialy

    Giovanni Alberti

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  1. Giovanni Alberti
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Alberti, G. On the structure of singular sets of convex functions. Calc. Var 2, 17–27 (1994). https://doi.org/10.1007/BF01234313

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  • DOI: https://doi.org/10.1007/BF01234313

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