Regularity criteria for the surface growth model with a forcing term

Abstract

Based on a compactness method, we establish regularity criteria for suitable weak solutions to the surface growth model with a forcing term. These criteria imply that the H\"older regularity of solutions follows from smallness conditions on several scale-invariant quantities. As a consequence, we obtain a partial regularity result stating that the one-dimensional biparabolic Hausdorff measure of the singular set is zero.