On differentiability of Sobolev functions with respect to the Sobolev norm

Vladimir Gol'dshtein; Paz Hashash; Alexander Ukhlov

On differentiability of Sobolev functions with respect to the Sobolev norm

Analysis of PDEs 2023-11-30 v3

Authors: Vladimir Gol'dshtein , Paz Hashash , Alexander Ukhlov

Abstract

We study connections between the $W^1_p$ -differentiability and the $L_p$ -differentiability of Sobolev functions. We prove that, $W^1_p$ -differentiability implies the $L_p$ -differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the $W^1_p$ -differentiability of Sobolev functions $\cp_p$ -almost everywhere.

Keywords

sobolev functions w1p-differentiability lp-differentiability approximate differentiability sobolev norm cp-almost everywhere

Cite

@article{arxiv.2207.08738,
  title  = {On differentiability of Sobolev functions with respect to the Sobolev norm},
  author = {Vladimir Gol'dshtein and Paz Hashash and Alexander Ukhlov},
  journal= {arXiv preprint arXiv:2207.08738},
  year   = {2023}
}

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20 pages

On differentiability of Sobolev functions with respect to the Sobolev norm

Abstract

Keywords

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