Laguerre BV spaces, Laguerre perimeter and their applications

He Wang; Yu Liu; He Wang; Yu Liu

doi:10.3934/cam.2023011

Communications in Analysis and Mechanics

2023, Volume 15, Issue 2: 189-213. doi: 10.3934/cam.2023011

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Research article Special Issues

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

Received: 31 March 2023 Revised: 05 May 2023 Accepted: 05 May 2023 Published: 12 May 2023
26A45, 46E35, 33C45

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.
- BV space,
- perimeter,
- isoperimetric inequality,
- Sobolev inequality,
- Laguerre operator
Citation: He Wang, Yu Liu. Laguerre BV spaces, Laguerre perimeter and their applications[J]. Communications in Analysis and Mechanics, 2023, 15(2): 189-213. doi: 10.3934/cam.2023011

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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.

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