We study mappings $f : (a, b) \to Y$ with finite dilation having Lebesgueintegrable majorant, where $Y$ is a real normed vector space. We construct Lipschitz mapping $f : (a, b) \to Y$, $\rm{dim}Y = \infty$, which is nowhere differentiable but its graph has everywhere trivial contingent. We show that if the contingent of the graph of a mapping with finite dilation is a nontrivial space, then $f$ is almost everywhere differentiable.
@article{348,
title = {On differentiability of mappings with finite dilation},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v62i0.348},
language = {EN},
url = {http://dml.mathdoc.fr/item/348}
}
Turowska, Małgorzata. On differentiability of mappings with finite dilation. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v62i0.348. http://gdmltest.u-ga.fr/item/348/