Regularity criteria for the surface growth model with a forcing term

Yuqian Cheng; Zhisu Li; Xuening Wei

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arXiv · 2603.12714

Regularity criteria for the surface growth model with a forcing term

Yuqian Cheng·Zhisu Li·Xuening Wei

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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.

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Yuqian Cheng, Zhisu Li, Xuening Wei. 2026-03-13. Regularity criteria for the surface growth model with a forcing term. https://arxiv.org/abs/2603.12714

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