The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910459774369792 |
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| author | Dong, Weisong Niu, Jinling Nizhamuding, Nadilamu |
| author_facet | Dong, Weisong Niu, Jinling Nizhamuding, Nadilamu |
| contents | In this paper, we study the Dirichlet problem for Monge-Ampère type equations for $p$-plurisubharmonic functions on Riemannian manifolds. The $a$ $priori$ estimates up to the second order derivatives of solutions are established. The existence of a solution then follows by the continuity method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds Dong, Weisong Niu, Jinling Nizhamuding, Nadilamu Analysis of PDEs 35J15, 35B45 In this paper, we study the Dirichlet problem for Monge-Ampère type equations for $p$-plurisubharmonic functions on Riemannian manifolds. The $a$ $priori$ estimates up to the second order derivatives of solutions are established. The existence of a solution then follows by the continuity method. |
| title | The Dirichlet problem for Monge-Ampère type equations on Riemannian manifolds |
| topic | Analysis of PDEs 35J15, 35B45 |
| url | https://arxiv.org/abs/2405.11925 |