Journal of the European Mathematical Society

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Volume 12, Issue 2, 2010, pp. 385–412
DOI: 10.4171/JEMS/202

Fréchet differentiability of Lipschitz functions via a variational principle

Joram Lindenstrauss[1], David Preiss[2] and Jaroslav Tišer[3]

(1) Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel
(2) Department of Mathematics, University of Warwick, CV4 7AL, Coventry, UK
(3) Department of Mathematics, Czech Technical University, Thakurova 7, 166 27, Prague 6, Czechia

We prove a new variational principle which in particular does not assume the completeness of the domain. As an application we give a new, more natural, proof of the fact that a real valued Lipschitz function on an Asplund space has points of Fréchet differentiability.

Keywords: Fréchet differentiability, Lipschitz functions, variational principle, Asplund space, mean value theorem, (d,d0)-complete metric space, cone monotone functions

Lindenstrauss Joram, Preiss David, Tišer Jaroslav: Fréchet differentiability of Lipschitz functions via a variational principle. J. Eur. Math. Soc. 12 (2010), 385-412. doi: 10.4171/JEMS/202