Anisotropic coarsening: Grain shapes and nonuniversal persistence

We solve a coarsening system with small but arbitrary anisotropic surface t ension and interface mobility. The resulting size-dependent growth shapes a re significantly different from equilibrium microcrystallites, and have a d istribution of grain sizes different from isotropic theories. As an applica tion of our results, we show that the persistence decay exponent depends on anisotropy and, hence, is nonuniversal.