On velocity selection for needle-crystals in a fully non-local model of solidification

We show that the results on velocity selection for needle-crystals in the symmetric model of dendritic solidification recently derived by Ben Amar-Pomeau [8] and by Barbieri, Hong and Langer [11] in the small Péclet number p limit, are in fact strictly valid for all p's. This means, in particular, that for 2-D systems with a weakly anisotropic surface tension, the selected velocity should scale as p2 for all undercoolings.