Weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders

TL;DR

This paper establishes weighted Dirichlet-type inequalities and a weighted isoperimetric inequality for decreasing rearrangements within cylindrical domains.

Contribution

It introduces new weighted inequalities specific to decreasing rearrangements in cylinders, extending classical isoperimetric results.

Findings

Proved weighted Dirichlet-type inequalities in cylindrical settings

Derived a weighted isoperimetric inequality for decreasing rearrangements

Extended classical inequalities to weighted cylindrical domains

Abstract

In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.