Laguerre BV spaces, Laguerre perimeter and their applications

TL;DR

This paper introduces Laguerre BV spaces and perimeter, explores their properties, and establishes key inequalities and applications, including mean curvature, within the Laguerre mathematical framework.

Contribution

It defines Laguerre BV spaces and perimeter, proving fundamental inequalities and deriving mean curvature, advancing the mathematical understanding of Laguerre analysis.

Findings

Established the Laguerre isoperimetric inequality

Proved the Sobolev inequality in the Laguerre setting

Derived the mean curvature for Laguerre perimeter

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.