Optimal regularity for degenerate elliptic equations with Hamiltonian terms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916883277545472 |
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| author | Andrade, Pêdra D. S. Nascimento, Thialita M. |
| author_facet | Andrade, Pêdra D. S. Nascimento, Thialita M. |
| contents | We establish optimal, quantitative Höder estimates for the gradient of solutions to a class of degenerate elliptic equations with Hamiltonian terms. The presence of such lower-order terms introduces additional challenges, particularly in regimes where the gradient is either very small or very large. Our approach adapts perturbative techniques to capture the interplay between the degeneracy rate and the Hamiltonian's growth. Our results naturally extend the regularity theory developed by Araujo-Ricarte-Teixeira (Calc. Var. 53:605-625, 2015) and Birindelli-Demengel (Nonlinear Differ. Equ. Appl. 23:41, 2016) to a more general setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal regularity for degenerate elliptic equations with Hamiltonian terms Andrade, Pêdra D. S. Nascimento, Thialita M. Analysis of PDEs We establish optimal, quantitative Höder estimates for the gradient of solutions to a class of degenerate elliptic equations with Hamiltonian terms. The presence of such lower-order terms introduces additional challenges, particularly in regimes where the gradient is either very small or very large. Our approach adapts perturbative techniques to capture the interplay between the degeneracy rate and the Hamiltonian's growth. Our results naturally extend the regularity theory developed by Araujo-Ricarte-Teixeira (Calc. Var. 53:605-625, 2015) and Birindelli-Demengel (Nonlinear Differ. Equ. Appl. 23:41, 2016) to a more general setting. |
| title | Optimal regularity for degenerate elliptic equations with Hamiltonian terms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.03924 |