  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.
