The static color-Coulomb interaction potential is calculated as the so
lution of a nonlinear integral equation which arises in the Hamiltonia
n Coulomb gauge when the restriction to the interior of the Gribov hor
izon is implemented. The potential obtained is in qualitative agreemen
t with expectations, being Coulombic with logarithmic corrections at s
hort range, and confining at long range. The values obtained for the s
tring tension and Lambda<(MS)over bar> are in semiquantitative agreeme
nt with lattice Monte Carlo and phenomenological determinations.