Uniform estimates and Brezis-Merle type inequalities for the $k$-Hessian equation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910171742076928 |
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| author | Deng, Jie Wang, Haibin Zhou, Bin |
| author_facet | Deng, Jie Wang, Haibin Zhou, Bin |
| contents | In this paper, we prove a Brezis-Merle type inequality for $k$-convex functions vanishing on the boundary. As an application, we establish an Alexandrov-Bakelman-Pucci type estimate for the intermediate Hessian equation. Furthermore, we establish a concentration-compactness principle for the blow-up behavior of solutions to the mean field type $k$-Hessian equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25511 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform estimates and Brezis-Merle type inequalities for the $k$-Hessian equation Deng, Jie Wang, Haibin Zhou, Bin Analysis of PDEs 35J96, 35B44 In this paper, we prove a Brezis-Merle type inequality for $k$-convex functions vanishing on the boundary. As an application, we establish an Alexandrov-Bakelman-Pucci type estimate for the intermediate Hessian equation. Furthermore, we establish a concentration-compactness principle for the blow-up behavior of solutions to the mean field type $k$-Hessian equation. |
| title | Uniform estimates and Brezis-Merle type inequalities for the $k$-Hessian equation |
| topic | Analysis of PDEs 35J96, 35B44 |
| url | https://arxiv.org/abs/2603.25511 |