  We develop a Coulomb gas formalism for boundary conformal field theory having
a $W$ symmetry and illustrate its operation using the three state Potts model.
We find that there are free-field representations for six $W$ conserving
boundary states, which yield the fixed and mixed physical boundary conditions,
and two $W$ violating boundary states which yield the free and new boundary
conditions. Other $W$ violating boundary states can be constructed but they
decouple from the rest of the theory. Thus we have a complete free-field
realization of the known boundary states of the three state Potts model. We
then use the formalism to calculate boundary correlation functions in various
cases. We find that the conformal blocks arising when the two point function of
$\phi_{2,3}$ is calculated in the presence of free and new boundary conditions
are indeed the last two solutions of the sixth order differential equation
generated by the singular vector.
