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.