A Note on Differentiability of Lipschitz Maps

Rafał Górak. "A Note on Differentiability of Lipschitz Maps." Bulletin of the Polish Academy of Sciences. Mathematics 58.3 (2010): 259-268. <http://eudml.org/doc/281216>.

@article{RafałGórak2010,
abstract = {We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.},
author = {Rafał Górak},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {scattered compactum; point of Fréchet differentiability; Lipschitz functions},
language = {eng},
number = {3},
pages = {259-268},
title = {A Note on Differentiability of Lipschitz Maps},
url = {http://eudml.org/doc/281216},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Rafał Górak
TI - A Note on Differentiability of Lipschitz Maps
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 3
SP - 259
EP - 268
AB - We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
LA - eng
KW - scattered compactum; point of Fréchet differentiability; Lipschitz functions
UR - http://eudml.org/doc/281216
ER -