Sharp regularity for degenerate fully nonlinear equations with oblique boundary conditions and Hamiltonian terms
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915978321854464 |
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| author | Bessa, Junior da Silva Ricarte, Gleydson C. |
| author_facet | Bessa, Junior da Silva Ricarte, Gleydson C. |
| contents | We prove optimal boundary $C^{1,α}$ regularity for viscosity solutions of degenerate fully nonlinear uniformly elliptic equations with oblique boundary conditions and Hamiltonian terms of the form \[ \begin{cases} |Du|^γF(D^2 u) + \varrho(x)|Du|^σ = f(x) & \text{in } Ω,\\ β(x)\cdot Du+ζ(x)u = g(x) & \text{on } \partial Ω, \end{cases} \] where $γ>0$ and $0<σ\le 1+γ$. We develop a compactness framework for affine translations, linking the size of the translation to the Hamiltonian structure. This is combined with a boundary improvement-of-flatness argument adapted to oblique boundary data, yielding the optimal boundary regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02855 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp regularity for degenerate fully nonlinear equations with oblique boundary conditions and Hamiltonian terms Bessa, Junior da Silva Ricarte, Gleydson C. Analysis of PDEs We prove optimal boundary $C^{1,α}$ regularity for viscosity solutions of degenerate fully nonlinear uniformly elliptic equations with oblique boundary conditions and Hamiltonian terms of the form \[ \begin{cases} |Du|^γF(D^2 u) + \varrho(x)|Du|^σ = f(x) & \text{in } Ω,\\ β(x)\cdot Du+ζ(x)u = g(x) & \text{on } \partial Ω, \end{cases} \] where $γ>0$ and $0<σ\le 1+γ$. We develop a compactness framework for affine translations, linking the size of the translation to the Hamiltonian structure. This is combined with a boundary improvement-of-flatness argument adapted to oblique boundary data, yielding the optimal boundary regularity. |
| title | Sharp regularity for degenerate fully nonlinear equations with oblique boundary conditions and Hamiltonian terms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.02855 |