Liouville type theorems for fully nonlinear elliptic equations in exterior domains in half spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914607382134784 |
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| author | Li, Dongsheng Liu, Rulin |
| author_facet | Li, Dongsheng Liu, Rulin |
| contents | We establish a Liouville type theorem for fully nonlinear uniformly elliptic equations in exterior domains in half spaces under quadratic boundary data and a quadratic growth condition, that is, any viscosity solution tends to a quadratic polynomial plus lower order terms at infinity with the rate at least $|x|^{-α-n}$ for any $α\in(0,1)$. As applications, this result can lead to Liouville type theorems for Monge-Amp`ere equations, k-Hessian equations and special Lagrangian equations with critical and supercritical phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouville type theorems for fully nonlinear elliptic equations in exterior domains in half spaces Li, Dongsheng Liu, Rulin Analysis of PDEs We establish a Liouville type theorem for fully nonlinear uniformly elliptic equations in exterior domains in half spaces under quadratic boundary data and a quadratic growth condition, that is, any viscosity solution tends to a quadratic polynomial plus lower order terms at infinity with the rate at least $|x|^{-α-n}$ for any $α\in(0,1)$. As applications, this result can lead to Liouville type theorems for Monge-Amp`ere equations, k-Hessian equations and special Lagrangian equations with critical and supercritical phases. |
| title | Liouville type theorems for fully nonlinear elliptic equations in exterior domains in half spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.28199 |