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.