Quadratic growth solutions of fully nonlinear elliptic equations with periodic data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909975568187392 |
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| author | Li, Dongsheng Liang, Lichun |
| author_facet | Li, Dongsheng Liang, Lichun |
| contents | In this paper, we study quadratic growth solutions $u$ of fully nonlinear elliptic equations of the form $F(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is periodic and $F$ may be not uniformly elliptic. The existence of solutions and Liouville type results in the whole space and exterior domains are established, which generalize the classical results when $f$ is constant. As applications, the corresponding results are given to $k$-Hessian equations, which include the celebrated results for Monge-Ampère equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_13927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic growth solutions of fully nonlinear elliptic equations with periodic data Li, Dongsheng Liang, Lichun Analysis of PDEs In this paper, we study quadratic growth solutions $u$ of fully nonlinear elliptic equations of the form $F(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is periodic and $F$ may be not uniformly elliptic. The existence of solutions and Liouville type results in the whole space and exterior domains are established, which generalize the classical results when $f$ is constant. As applications, the corresponding results are given to $k$-Hessian equations, which include the celebrated results for Monge-Ampère equations. |
| title | Quadratic growth solutions of fully nonlinear elliptic equations with periodic data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.13927 |