  The ground state energy of a binary mixture of Bose-Einstein condensates can
be estimated for large atomic samples by making use of suitably regularized
Thomas-Fermi density profiles. By exploiting a variational method on the trial
densities the energy can be computed by explicitly taking into account the
normalization condition. This yields analytical results and provides the basis
for further improvement of the approximation. As a case study, we consider a
binary mixture of $^{87}$Rb atoms in two different hyperfine states in a double
well potential and discuss the energy crossing between density profiles with
different numbers of domain walls, as the number of particles and the
inter-species interaction vary.
