Boundary $C^{2, α}$ Regularity for the Oblique Boundary Value Problem of Monge-Ampère Equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909118530322432 |
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| author | Jian, Huaiyu Tu, Xushan |
| author_facet | Jian, Huaiyu Tu, Xushan |
| contents | We study the good shape property of boundary sections of convex solutions of the oblique boundary value problem for Monge-Ampère equations $$\det D^2u =f(x) \text{ in } Ω, \quad D_βu = ϕ(x) \text{ on } \partial Ω.$$ In the two-dimensional case, we prove the global $C^{2,α}$ estimate for the solution. When the dimension $n \geq 3$, we show that this estimate still holds if the solution is bounded from above by a quadratic function in the tangent direction. We also obtain an existence result for the convex solution of Monge-Ampère equations with Robin oblique boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_09765 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Boundary $C^{2, α}$ Regularity for the Oblique Boundary Value Problem of Monge-Ampère Equations Jian, Huaiyu Tu, Xushan Analysis of PDEs 35J60, 35J96, 35J25 We study the good shape property of boundary sections of convex solutions of the oblique boundary value problem for Monge-Ampère equations $$\det D^2u =f(x) \text{ in } Ω, \quad D_βu = ϕ(x) \text{ on } \partial Ω.$$ In the two-dimensional case, we prove the global $C^{2,α}$ estimate for the solution. When the dimension $n \geq 3$, we show that this estimate still holds if the solution is bounded from above by a quadratic function in the tangent direction. We also obtain an existence result for the convex solution of Monge-Ampère equations with Robin oblique boundary conditions. |
| title | Boundary $C^{2, α}$ Regularity for the Oblique Boundary Value Problem of Monge-Ampère Equations |
| topic | Analysis of PDEs 35J60, 35J96, 35J25 |
| url | https://arxiv.org/abs/2111.09765 |