# Uniqueness and radial symmetry of minimizers for a nonlocal variational problem

## TL;DR

This paper proves that minimizers for certain nonlocal variational problems are unique and radially symmetric, using Fourier transform techniques, which advances understanding of these models in various phenomena.

## Contribution

It establishes the uniqueness and radial symmetry of minimizers for nonlocal variational problems, employing Fourier transform methods, which is a novel approach in this context.

## Key findings

- Minimizers are unique due to the convexity of the functional.
- Minimizers exhibit radial symmetry.
- Fourier transform of tempered distributions is used as the main technique.

## Abstract

In this paper we prove the uniqueness and radial symmetry of minimizers for variational problems that model several phenomena. The uniqueness is a consequence of the convexity of the functional. The main technique is Fourier transform of tempered distributions.