$C^{1,α}$ regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on $C^1$ domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929404679028736 |
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| author | Byun, Sun-Sig Kim, Hongsoo Oh, Jehan |
| author_facet | Byun, Sun-Sig Kim, Hongsoo Oh, Jehan |
| contents | We provide a sharp $C^{1,α}$ estimate up to the boundary for a viscosity solution of a degenerate fully nonlinear elliptic equation with the oblique boundary condition on a $C^1$ domain. To this end, we first obtain a uniform boundary H{ö}lder estimate with the oblique boundary condition in an "almost $C^1$-flat" domain for the equations which is uniformly elliptic only where the gradient is far from some point, and then we establish a desired $C^{1,α}$ regularity based on perturbation and compactness arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^{1,α}$ regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on $C^1$ domains Byun, Sun-Sig Kim, Hongsoo Oh, Jehan Analysis of PDEs 35J25, 35B65, 35D40, 35J60, 35J70 We provide a sharp $C^{1,α}$ estimate up to the boundary for a viscosity solution of a degenerate fully nonlinear elliptic equation with the oblique boundary condition on a $C^1$ domain. To this end, we first obtain a uniform boundary H{ö}lder estimate with the oblique boundary condition in an "almost $C^1$-flat" domain for the equations which is uniformly elliptic only where the gradient is far from some point, and then we establish a desired $C^{1,α}$ regularity based on perturbation and compactness arguments. |
| title | $C^{1,α}$ regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on $C^1$ domains |
| topic | Analysis of PDEs 35J25, 35B65, 35D40, 35J60, 35J70 |
| url | https://arxiv.org/abs/2407.01061 |