Towards optimal regularity for the fourth-order thin film equation in $\re^N$: Graveleau-type focusing self-similarity

Pablo Alvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov

An approach to some "optimal" (more precisely, non-improvable) regularity of solutions of the thin film equation u_{t} = -\nabla \cdot(|u|^{n} \nabla \D u) in \ren \times \re_+, u(…