The exterior Dirichlet problem for the homogeneous complex k-Hessian equation
In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradie...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-01-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2022-0039 |
| _version_ | 1811171904887717888 |
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| author | Gao Zhenghuan Ma Xinan Zhang Dekai |
| author_facet | Gao Zhenghuan Ma Xinan Zhang Dekai |
| author_sort | Gao Zhenghuan |
| collection | DOAJ |
| description | In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate. |
| first_indexed | 2024-04-10T17:23:03Z |
| format | Article |
| id | doaj.art-ba2a4ae044854094a9a3625bb584ab86 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-04-10T17:23:03Z |
| publishDate | 2023-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-ba2a4ae044854094a9a3625bb584ab862023-02-05T08:43:35ZengDe GruyterAdvanced Nonlinear Studies2169-03752023-01-01231518510.1515/ans-2022-0039The exterior Dirichlet problem for the homogeneous complex k-Hessian equationGao Zhenghuan0Ma Xinan1Zhang Dekai2Department of Mathematics, Shanghai University, Shanghai, 200444, ChinaSchool of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui Province, ChinaDepartment of Mathematics, Shanghai University, Shanghai, 200444, ChinaIn this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.https://doi.org/10.1515/ans-2022-0039exterior dirichlet problemcomplex k-hessian equationk-subharmonic functiongradient estimate35b6535j25 |
| spellingShingle | Gao Zhenghuan Ma Xinan Zhang Dekai The exterior Dirichlet problem for the homogeneous complex k-Hessian equation Advanced Nonlinear Studies exterior dirichlet problem complex k-hessian equation k-subharmonic function gradient estimate 35b65 35j25 |
| title | The exterior Dirichlet problem for the homogeneous complex k-Hessian equation |
| title_full | The exterior Dirichlet problem for the homogeneous complex k-Hessian equation |
| title_fullStr | The exterior Dirichlet problem for the homogeneous complex k-Hessian equation |
| title_full_unstemmed | The exterior Dirichlet problem for the homogeneous complex k-Hessian equation |
| title_short | The exterior Dirichlet problem for the homogeneous complex k-Hessian equation |
| title_sort | exterior dirichlet problem for the homogeneous complex k hessian equation |
| topic | exterior dirichlet problem complex k-hessian equation k-subharmonic function gradient estimate 35b65 35j25 |
| url | https://doi.org/10.1515/ans-2022-0039 |
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