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Research Article | Open Access

Laguerre BV spaces, Laguerre perimeter and their applications

He Wang, Yu Liu( )
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
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Abstract

In this paper, we introduce the Laguerre bounded variation space and the Laguerre perimeter, thereby investigating their properties. Moreover, we prove the isoperimetric inequality and the Sobolev inequality in the Laguerre setting. As applications, we derive the mean curvature for the Laguerre perimeter.

Keywords

BV spaceperimeterisoperimetric inequalitySobolev inequalityLaguerre operator
CLC number: 26A45, 46E35, 33C45

References

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Communications in Analysis and Mechanics
Volume 15 Issue 2,
June 2023
Pages 189-213
DOI: 10.3934/cam.2023011

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Wang H, Liu Y. Laguerre BV spaces, Laguerre perimeter and their applications. Communications in Analysis and Mechanics, 2023, 15(2): 189-213. https://doi.org/10.3934/cam.2023011

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Received: 31 March 2023
Revised: 05 May 2023
Accepted: 05 May 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

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