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

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 - Gol'dshtein, Vladimir

AU - Hashash, Paz

AU - Ukhlov, Alexander

PY - 2024/10/1

Y1 - 2024/10/1

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.

KW - Sobolev spaces

KW - potential theory

UR - https://www.scopus.com/pages/publications/85199170938

U2 - 10.1002/mana.202300545

DO - 10.1002/mana.202300545

M3 - Article

AN - SCOPUS:85199170938

SN - 0025-584X

VL - 297

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JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 10

ER -

On differentiability of Sobolev functions with respect to the Sobolev norm

Abstract

Keywords

ASJC Scopus subject areas

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