Velocity selection in dendritic growth

We show that the velocity and shape of two-dimensional dendritic crystals can be determined by solving the steady-state evolution equation at finite surface tension. We find that in the zero undercooling limit, crystal anisotropy is necessary to obtain finite velocities. Furthermore, the " solvability" condition at zero anisotropy and small undercooling is essentially singular in the velocity. Finally, we comment on the extension of our results to finite Peclet number and to three dimensions.