Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908257461731328 |
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| author | Lee, Se-Chan Lian, Yuanyuan Yun, Hyungsung Zhang, Kai |
| author_facet | Lee, Se-Chan Lian, Yuanyuan Yun, Hyungsung Zhang, Kai |
| contents | We establish the boundedness of time derivatives of solutions to parabolic $p$-Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximation method. As a consequence, we obtain an optimal regularity result with a connection to the well-known $C^{p'}$-conjecture in the elliptic setting. Finally, we extend our method to treat global regularity results for both fully nonlinear and general quasilinear degenerate parabolic problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity Lee, Se-Chan Lian, Yuanyuan Yun, Hyungsung Zhang, Kai Analysis of PDEs 35B65, 35D40, 35K92, 35K65 We establish the boundedness of time derivatives of solutions to parabolic $p$-Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximation method. As a consequence, we obtain an optimal regularity result with a connection to the well-known $C^{p'}$-conjecture in the elliptic setting. Finally, we extend our method to treat global regularity results for both fully nonlinear and general quasilinear degenerate parabolic problems. |
| title | Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity |
| topic | Analysis of PDEs 35B65, 35D40, 35K92, 35K65 |
| url | https://arxiv.org/abs/2503.04384 |