Bobkov's inequality via optimal control theory

TL;DR

This paper presents a straightforward proof of Bobkov's inequality leveraging dynamical programming, providing a new perspective and characterizing the optimizers involved.

Contribution

It introduces a novel proof technique for Bobkov's inequality using optimal control theory and offers a characterization of the optimizers.

Findings

Simplified proof of Bobkov's inequality

Characterization of the optimizers involved

Application of dynamical programming principle

Abstract

We give the simple proof of Bobkov's inequality using the arguments of dynamical programming principle. As a byproduct of the method we obtain a characterization of optimizers.