Regularity criteria for the surface growth model with a forcing term

TL;DR

This paper develops regularity criteria for solutions to a surface growth model with forcing, showing that small scale-invariant quantities ensure regularity and that the singular set has zero measure.

Contribution

It introduces new regularity criteria based on scale-invariant quantities for the surface growth model with forcing.

Findings

Solutions are H"older continuous under smallness conditions.

The singular set has zero one-dimensional biparabolic Hausdorff measure.

Partial regularity results are established for the model.

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.