On differentiability of mappings with finite dilation
Abstract
We study mappings $f : (a, b) \to Y$ with finite dilation having Lebesgue
integrable 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.
integrable 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.
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PDFDOI: https://doi.org/10.2478/tatra.v62i0.348