Sharp regularity for a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911643258060800 |
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| author | Huo, Wentao Jin, Xiaofeng Ma, Lingwei Zhang, Zhenqiu |
| author_facet | Huo, Wentao Jin, Xiaofeng Ma, Lingwei Zhang, Zhenqiu |
| contents | We investigate the regularity of the viscosity solutions to a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms. To overcome the difficulty caused by the simultaneous presence of the general degenerate/singular gradient terms and Hamiltonian terms, we analyze the coupled interplay between the degeneracy/singularity law and the growth of Hamiltonian terms and establish lower regularity results. Finally, we obtain sharp interior $C^{1,α}$ regularity estimates via a geometric tangential method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02345 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp regularity for a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms Huo, Wentao Jin, Xiaofeng Ma, Lingwei Zhang, Zhenqiu Analysis of PDEs 35B65, 35J60, 35J70, 35J75, 35D40 We investigate the regularity of the viscosity solutions to a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms. To overcome the difficulty caused by the simultaneous presence of the general degenerate/singular gradient terms and Hamiltonian terms, we analyze the coupled interplay between the degeneracy/singularity law and the growth of Hamiltonian terms and establish lower regularity results. Finally, we obtain sharp interior $C^{1,α}$ regularity estimates via a geometric tangential method. |
| title | Sharp regularity for a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms |
| topic | Analysis of PDEs 35B65, 35J60, 35J70, 35J75, 35D40 |
| url | https://arxiv.org/abs/2605.02345 |