  We investigate the composition and the equation of state of the kaon
condensed phase in neutrino-free and neutrino-trapped star matter within the
framework of the Brueckner-Hartree-Fock approach with three-body forces. We
find that neutrino trapping shifts the onset density of kaon condensation to a
larger baryon density, and reduces considerably the kaon abundance. As a
consequence, when kaons are allowed, the equation of state of neutrino-trapped
star matter becomes stiffer than the one of neutrino free matter. The effects
of different three-body forces are compared and discussed. Neutrino trapping
turns out to weaken the role played by the symmetry energy in determining the
composition of stellar matter, and thus reduces the difference between the
results obtained by using different three-body forces.
