A gradient type term for the $k$-Hessian equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914733609713664 |
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| author | Cardoso, Mykael de Araújo Sousa, Jefferson de Brito de Oliveira, José Francisco |
| author_facet | Cardoso, Mykael de Araújo Sousa, Jefferson de Brito de Oliveira, José Francisco |
| contents | In this paper, we propose a gradient type term for the $k$-Hessian equation that extends for $k>1$ the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan-Kramer change of variables. As applications, we ensure the existence of solutions for a new class of $k$-Hessian equation in the sublinear and superlinear cases for Sobolev type growth. The threshold for existence is obtained in some particular cases. In addition, for the Trudinger-Moser type growth regime, we also prove the existence of solutions under either subcritical or critical conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07201 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A gradient type term for the $k$-Hessian equation Cardoso, Mykael de Araújo Sousa, Jefferson de Brito de Oliveira, José Francisco Analysis of PDEs 35J66, 35J60, 35J50, 35J96 In this paper, we propose a gradient type term for the $k$-Hessian equation that extends for $k>1$ the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan-Kramer change of variables. As applications, we ensure the existence of solutions for a new class of $k$-Hessian equation in the sublinear and superlinear cases for Sobolev type growth. The threshold for existence is obtained in some particular cases. In addition, for the Trudinger-Moser type growth regime, we also prove the existence of solutions under either subcritical or critical conditions. |
| title | A gradient type term for the $k$-Hessian equation |
| topic | Analysis of PDEs 35J66, 35J60, 35J50, 35J96 |
| url | https://arxiv.org/abs/2301.07201 |