# A sharp weighted anisotropic Poincar\'e inequality for convex domains

## TL;DR

This paper establishes an optimal lower bound for the best constant in a class of weighted anisotropic Poincaré inequalities specifically for convex domains, advancing the understanding of these inequalities in geometric analysis.

## Contribution

It provides a sharp, optimal lower bound for the weighted anisotropic Poincaré inequality constants on convex domains, which was previously unknown.

## Key findings

- Derived an optimal lower bound for the inequality constant
- Enhanced understanding of anisotropic Poincaré inequalities in convex geometry
- Potential applications in geometric analysis and PDEs

## Abstract

We prove an optimal lower bound for the best constant in a class of weighted anisotropic Poincar\'e inequalities