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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03231 |
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| _version_ | 1866915275330289664 |
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| author | He, Rongxun Huang, Genggeng |
| author_facet | He, Rongxun Huang, Genggeng |
| contents | In this paper, we study the existence and uniqueness of solutions to the weighted eigenvalue problem for $k$-Hessian equation. To achieve this, we establish the uniform a priori estimates for gradient and second derivatives of solutions to Hessian equation with weight $|x|^{2sk}$ on the right-hand-side. We also prove that the eigenfunction is a minimizer of the corresponding functional among all $k$-admissible functions vanishing on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Eigenvalue Problem for a Class of Hessian Equations He, Rongxun Huang, Genggeng Analysis of PDEs In this paper, we study the existence and uniqueness of solutions to the weighted eigenvalue problem for $k$-Hessian equation. To achieve this, we establish the uniform a priori estimates for gradient and second derivatives of solutions to Hessian equation with weight $|x|^{2sk}$ on the right-hand-side. We also prove that the eigenfunction is a minimizer of the corresponding functional among all $k$-admissible functions vanishing on the boundary. |
| title | Weighted Eigenvalue Problem for a Class of Hessian Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.03231 |