On differentiability of Sobolev functions with respect to the Sobolev norm

Pub Date : 2024-07-22 DOI:10.1002/mana.202300545

Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov

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Abstract

We study connections between the $W_{p}^{1}$ -differentiability and the $L_{p}$ -differentiability of Sobolev functions. We prove that $W_{p}^{1}$ -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 $W_{p}^{1}$ -differentiability of Sobolev functions ${cap}_{p}$ -almost everywhere.

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关于索波列函数与索波列规范的可微分性

我们研究索波列函数的-可微性与-可微性之间的联系。我们证明了-可微分性意味着-可微分性，但相反的暗示并不成立。我们还讨论了近似可微分性的概念。此外，我们还考虑了几乎无处不在的 Sobolev 函数的可微性。

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