Calculus of Variations and Geometric Measure Theory

N. Fusco - D. A. La Manna

Some weighted isoperimetric inequalities in quantitative form

created by lamanna on 19 Jul 2022
modified on 11 Jul 2023



Inserted: 19 jul 2022
Last Updated: 11 jul 2023

Year: 2022

ArXiv: 2207.06250 PDF


In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior of a negative power weight for the perimeter thus providing a complete picture of the isoperimetric problem in this context.