A Cahn–Hilliard equation with singular diffusion

In the present work, we address a class of Cahn–Hilliard equations characterized by a singular diffusion term. The problem is a simplified version with constant mobility of the Cahn–Hilliard–de Gennes model of phase separation in binary, incompressible, isothermal mixtures of polymer molecules. It is proved that, for any final time T, the problem admits a unique energy type weak solution, defined over (0,T). For any τ>0 such solution is classical in the sense of belonging to a suitable Hölder class over (τ,T), and enjoys the property of being separated from the singular values corresponding to pure phases.