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Beschreibung:
We prove existence of solutions to an anisotropic Cahn–Hilliard-type equation with degenerate diffusional mobility. In particular, the mobility vanishes at the pure phases, which is typically used to model motion by surface diffusion. The main difficulty of the present existence result is the strong non-linearity given by the fourth-order anisotropic operator. Imposing particular assumptions on the domain and assuming that the strength of the anisotropy is sufficiently small enables to establish appropriate bounds which allow to pass to the limit in the regularized problem. In addition to the existence we show that the absolute value of the corresponding solutions is bounded by 1.