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.