Critical and supercritical higher order parabolic problems in

A note on the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ involving critical exponent

“…Nonetheless, the local well posedness in H 1 (R N ) as in Proposition 1.1 applies only for ̺ not exceeding ̺ c and faster growing nonlinearities necessitate a separate treatment (see e.g. [16] and [34]).…”