Neumann Problems for Elliptic and Parabolic Sum Hessian Equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917979172634624 |
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| author | Liang, Weizhao Yan, Jin Zhu, Hua |
| author_facet | Liang, Weizhao Yan, Jin Zhu, Hua |
| contents | This paper studies the Neumann boundary value problem for sum Hessian equations. We first derive a priori $C^2$ estimates for $(k-1)$-admissible solutions in almost convex and uniformly $(k-1)$-convex domains, and prove the existence of admissible solutions via the method of continuity. Furthermore, we obtain existence results for the classical Neumann problem in uniformly convex domains. Finally, we extend these results to the corresponding parabolic problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neumann Problems for Elliptic and Parabolic Sum Hessian Equations Liang, Weizhao Yan, Jin Zhu, Hua Analysis of PDEs This paper studies the Neumann boundary value problem for sum Hessian equations. We first derive a priori $C^2$ estimates for $(k-1)$-admissible solutions in almost convex and uniformly $(k-1)$-convex domains, and prove the existence of admissible solutions via the method of continuity. Furthermore, we obtain existence results for the classical Neumann problem in uniformly convex domains. Finally, we extend these results to the corresponding parabolic problems. |
| title | Neumann Problems for Elliptic and Parabolic Sum Hessian Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.05025 |