On the Hessian Hardy-Sobolev Inequality and Related Variational Problems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909602239479808 |
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| author | He, Rongxun Ke, Wei |
| author_facet | He, Rongxun Ke, Wei |
| contents | In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study the existence and regularity results of solutions to related variational problems. Our results extend the variational theory of the Hessian equation in \cite{CW01variational}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Hessian Hardy-Sobolev Inequality and Related Variational Problems He, Rongxun Ke, Wei Analysis of PDEs In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study the existence and regularity results of solutions to related variational problems. Our results extend the variational theory of the Hessian equation in \cite{CW01variational}. |
| title | On the Hessian Hardy-Sobolev Inequality and Related Variational Problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.03245 |