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arXiv · 2207.08738

On differentiability of Sobolev functions with respect to the Sobolev norm

Vladimir Gol'dshtein·Paz Hashash·Alexander Ukhlov
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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.

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Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov. 2022-07-18. On differentiability of Sobolev functions with respect to the Sobolev norm. https://arxiv.org/abs/2207.08738

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