Abstract. We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on Ê2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w* closure of the set of its points of Gâteaux differentiability is norm separable.
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Joram Lindenstrauss, David Preiss, A new proof of Fréchet differentiability of Lipschitz functions. J. Eur. Math. Soc. 2 (2000), no. 3, pp. 199–216DOI 10.1007/S100970000019