Partial Regularity for a Surface Growth Model
Partial Regularity for a Surface Growth Model
We prove two partial regularity results for the scalar equation $u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the physical process of molecular epitaxy. We show that the set of space-time singularities has (upper) box-counting dimension no larger than 7/6 and 1-dimensional (parabolic) Hausdorff measure zero. These parallel the results …