Laguerre BV spaces, Laguerre perimeter and their applications

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.

In this paper we systematicallyinvestigate the theory of the Laguerre bounded variation space. Our results may have some potential applications in PDEs and potential theory