Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung

Arkady Poliakovsky

doi:10.1016/j.jfa.2021.109312

Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung

Arkady Poliakovsky

Department of Mathematics

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

14 Scopus citations

Abstract

We provide answers to some questions raised in a recent work by H. Brezis, J. Van Schaftingen and P.-L. Yung [2,3] concerning the Gagliardo semi-norm |u|_W^s,q computed at s=1, when the strong L^q is replaced by weak L^q. In particular, we address generalization of the results in [2,3] for a general domain and non-smooth functions.

Original language	English
Article number	109312
Journal	Journal of Functional Analysis
Volume	282
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2021.109312
State	Published - 1 Feb 2022

Keywords

Sobolev spaces
Weak L space

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2021.109312

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abstract = "We provide answers to some questions raised in a recent work by H. Brezis, J. Van Schaftingen and P.-L. Yung [2,3] concerning the Gagliardo semi-norm |u|Ws,q computed at s=1, when the strong Lq is replaced by weak Lq. In particular, we address generalization of the results in [2,3] for a general domain and non-smooth functions.",

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AB - We provide answers to some questions raised in a recent work by H. Brezis, J. Van Schaftingen and P.-L. Yung [2,3] concerning the Gagliardo semi-norm |u|Ws,q computed at s=1, when the strong Lq is replaced by weak Lq. In particular, we address generalization of the results in [2,3] for a general domain and non-smooth functions.

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KW - Weak L space

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DO - 10.1016/j.jfa.2021.109312

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Some remarks on a formula for Sobolev norms due to Brezis, Van Schaftingen and Yung

Abstract

Keywords

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