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Research Article | Open Access

Some sharp Sobolev inequalities on B V ( R n )

Jin Dai( ), Shuang Mou
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, China
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Abstract

In this paper, some sharp Sobolev inequalities on B V ( R n ), the space of functions of bounded variation on R n , n ≥ 2, are deduced through the L p Brunn-Minkowski theory. We will prove that these inequalities can all imply the sharp Sobolev inequality on B V ( R n ).

Keywords

Sobolev inequalitiesfunctions of bounded variationoptimal constants
CLC number: 46B20, 46E35, 52A21

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16851-16868
DOI: 10.3934/math.2022925

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Cite this article:
Dai J, Mou S. Some sharp Sobolev inequalities on B V ( R n ). AIMS Mathematics, 2022, 7(9): 16851-16868. https://doi.org/10.3934/math.2022925

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Received: 09 May 2022
Revised: 28 June 2022
Accepted: 04 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)