Résumé : We prove that the set of real valued Lipschitz functions defined over fnite dimensional spaces whose Clarke subdifferential is maximal at every point contains a linear subspace of uncountable dimension. This result goes in the line of a previous result by J. Borwein and X. Wang that shows some type of density in a similar context. Nevertheless, contrary to that result, our aproach is constructive. Moreover, in our setting we establish the spaceability of this property in the set of Lipschitz continuous functions.

References
[1] A. Daniilidis and G. Flores. Linear structure of functions with maximal clarke subdi-erential. ArXiv preprint, 2018.