Regularity criteria for the surface growth model with a forcing term
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908883788759040 |
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| author | Cheng, Yuqian Li, Zhisu Wei, Xuening |
| author_facet | Cheng, Yuqian Li, Zhisu Wei, Xuening |
| contents | 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 Hölder 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12714 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularity criteria for the surface growth model with a forcing term Cheng, Yuqian Li, Zhisu Wei, Xuening Analysis of PDEs 35B65, 35K55, 35Q35 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 Hölder 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. |
| title | Regularity criteria for the surface growth model with a forcing term |
| topic | Analysis of PDEs 35B65, 35K55, 35Q35 |
| url | https://arxiv.org/abs/2603.12714 |