Boundary Regularity for Fully Nonlinear Parabolic equations on $C^{1,\mathrm{Dini}}$ Domains
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916891233091584 |
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| author | Dong, Jiqi Li, Xuemei Lian, Yuanyuan |
| author_facet | Dong, Jiqi Li, Xuemei Lian, Yuanyuan |
| contents | We establish the boundary pointwise Lipschitz regularity on exterior $C^{1,\mathrm{Dini}}$ domains and the Hopf lemma on interior $C^{1,\mathrm{Dini}}$ domains for fully nonlinear parabolic equations by a unified perturbation method. In fact, above two regularity hold for more general solution sets, i.e., the Pucci's class $S^*(λ, Λ, f)$. Furthermore, based on the boundary pointwise Lipschitz regularity, we obtain the global ${W}^{2,δ}$ regularity on exterior $C^{1,\mathrm{Dini}}$ domains for any $0<δ<1$, which is new even for the harmonic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Regularity for Fully Nonlinear Parabolic equations on $C^{1,\mathrm{Dini}}$ Domains Dong, Jiqi Li, Xuemei Lian, Yuanyuan Analysis of PDEs 35B30, 35B65, 35D40, 35K10, 35K55 We establish the boundary pointwise Lipschitz regularity on exterior $C^{1,\mathrm{Dini}}$ domains and the Hopf lemma on interior $C^{1,\mathrm{Dini}}$ domains for fully nonlinear parabolic equations by a unified perturbation method. In fact, above two regularity hold for more general solution sets, i.e., the Pucci's class $S^*(λ, Λ, f)$. Furthermore, based on the boundary pointwise Lipschitz regularity, we obtain the global ${W}^{2,δ}$ regularity on exterior $C^{1,\mathrm{Dini}}$ domains for any $0<δ<1$, which is new even for the harmonic functions. |
| title | Boundary Regularity for Fully Nonlinear Parabolic equations on $C^{1,\mathrm{Dini}}$ Domains |
| topic | Analysis of PDEs 35B30, 35B65, 35D40, 35K10, 35K55 |
| url | https://arxiv.org/abs/2508.08008 |