On differentiability of Sobolev functions with respect to the Sobolev norm

Vladimir Gol'dshtein; Paz Hashash; Alexander Ukhlov

doi:10.1002/mana.202300545

On differentiability of Sobolev functions with respect to the Sobolev norm

Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study connections between the (Formula presented.) -differentiability and the (Formula presented.) -differentiability of Sobolev functions. We prove that (Formula presented.) -differentiability implies the (Formula presented.) -differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the (Formula presented.) -differentiability of Sobolev functions (Formula presented.) -almost everywhere.

Original language	English
Pages (from-to)	3681-3699
Number of pages	19
Journal	Mathematische Nachrichten
Volume	297
Issue number	10
DOIs	https://doi.org/10.1002/mana.202300545
State	Published - 1 Oct 2024

Keywords

Sobolev spaces
potential theory

ASJC Scopus subject areas

General Mathematics

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10.1002/mana.202300545

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abstract = "We study connections between the (Formula presented.) -differentiability and the (Formula presented.) -differentiability of Sobolev functions. We prove that (Formula presented.) -differentiability implies the (Formula presented.) -differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the (Formula presented.) -differentiability of Sobolev functions (Formula presented.) -almost everywhere.",

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AU - Hashash, Paz

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N2 - We study connections between the (Formula presented.) -differentiability and the (Formula presented.) -differentiability of Sobolev functions. We prove that (Formula presented.) -differentiability implies the (Formula presented.) -differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the (Formula presented.) -differentiability of Sobolev functions (Formula presented.) -almost everywhere.

AB - We study connections between the (Formula presented.) -differentiability and the (Formula presented.) -differentiability of Sobolev functions. We prove that (Formula presented.) -differentiability implies the (Formula presented.) -differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the (Formula presented.) -differentiability of Sobolev functions (Formula presented.) -almost everywhere.

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KW - potential theory

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On differentiability of Sobolev functions with respect to the Sobolev norm

Abstract

Keywords

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