The Morse-Sard theorem for Clarke critical values

Luc Barbet (1) , Marc Dambrine (1, 2) , A. Daniilidis (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IPRA - Institut Pluridisciplinaire de Recherche Appliquée en génie pétrolier
3 UAB - Departament de Matemàtiques [Barcelona]

The Morse-Sard theorem states that the set of critical values of a Ck smooth function defined on a Euclidean space Rd has Lebesgue measure zero, provided k?d. This result is hereby extended for (generalized) critical values of continuous selections over a compactly indexed countable family of Ck functions: it is shown that these functions are Lipschitz continuous and the set of their Clarke critical values is null. © 2013 Elsevier Ltd.

Domaines: Equations aux dérivées partielles [math.AP]

Luc Barbet, Marc Dambrine, A. Daniilidis. The Morse-Sard theorem for Clarke critical values. Advances in Mathematics, 2013, pp.217-227. ⟨10.1016/j.aim.2013.03.024⟩. ⟨hal-00866954⟩