# Uniqueness and Non-Degeneracy of Minimizers of the Pekar Functional on a Ball

## TL;DR

This paper proves the uniqueness and non-degeneracy of minimizers for the Pekar functional on a three-dimensional ball, establishing a quadratic lower bound related to the distance from the minimizer.

## Contribution

It demonstrates the uniqueness and non-degeneracy of minimizers of the Pekar functional on a ball, providing a quadratic lower bound based on the Hessian's properties.

## Key findings

- Uniqueness of minimizers on the ball.
- Non-degeneracy of the Hessian at the minimizer.
- Quadratic lower bound in terms of distance to the minimizer.

## Abstract

We consider the Pekar functional on a ball in R^3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from non-degeneracy of the Hessian at the minimum.