Boundary $ C^{1}$ regularity for degenerate fully nonlinear elliptic equations on $ C^{2} $ domain
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916000339853312 |
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| author | Wang, Jiangwen Jiang, Feida |
| author_facet | Wang, Jiangwen Jiang, Feida |
| contents | In this article, we establish global regularity results ($ C^{0,γ}$, $ C^{0,1} $ and $ C^{1}$ estimates) for a class of degenerate fully nonlinear equation on $ C^{2} $-domain. This corresponds to the boundary counterpart of the interior $ C^{1}$ regularity results by \cite{APPT22} and \cite{AN25}. By example we show that $ C^{1,α} $ regularity of boundary datum is sharp within the scale of Hölder spaces. As a byproduct, we also provide global $ C^{1,β} $ regularity for a class singular fully nonlinear equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_10369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundary $ C^{1}$ regularity for degenerate fully nonlinear elliptic equations on $ C^{2} $ domain Wang, Jiangwen Jiang, Feida Analysis of PDEs In this article, we establish global regularity results ($ C^{0,γ}$, $ C^{0,1} $ and $ C^{1}$ estimates) for a class of degenerate fully nonlinear equation on $ C^{2} $-domain. This corresponds to the boundary counterpart of the interior $ C^{1}$ regularity results by \cite{APPT22} and \cite{AN25}. By example we show that $ C^{1,α} $ regularity of boundary datum is sharp within the scale of Hölder spaces. As a byproduct, we also provide global $ C^{1,β} $ regularity for a class singular fully nonlinear equation. |
| title | Boundary $ C^{1}$ regularity for degenerate fully nonlinear elliptic equations on $ C^{2} $ domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.10369 |