# Determination of AdS Monopole Wall via Minimization

## TL;DR

This paper addresses a minimization problem related to AdS monopole walls, proving the existence and uniqueness of solutions, and providing methods for their practical construction and asymptotic analysis.

## Contribution

It introduces a novel approach to determine AdS monopole walls through a shooting method and energy estimates, advancing understanding of their structure.

## Key findings

- Unique solution to the minimization problem established.
- Practical construction of solutions via shooting method demonstrated.
- Asymptotic behavior of the monopole wall analyzed in large coupling limit.

## Abstract

In this note we solve a minimization problem arising in a recent work of Bolognesi and Tong on the determination of an AdS monopole wall. We show that the problem has a unique solution. Although the solution cannot be obtained explicitly, we show that it may practically be constructed via a shooting method for which the correct shooting slope is unique. We also obtain some energy estimates which allow an asymptotic explicit determination of the monopole wall in a large coupling parameter limit.