One-dimensional symmetry results for semilinear equations and inequalities on half-spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911147275321344 |
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| author | Beuvin, Nicolas Farina, Alberto |
| author_facet | Beuvin, Nicolas Farina, Alberto |
| contents | We prove new one-dimensional symmetry results for non-negative solutions, possibly unbounded, to the semilinear equation $ -Δu= f(u)$ in the upper half-space $\mathbb{R}^{N}_{+}$. Some Liouville-type theorems are also proven in the case of differential inequalities in $\mathbb{R}^{N}_{+}$, even without imposing any boundary condition. Although subject to dimensional restrictions, our results apply to a broad family of functions $f$. In particular, they apply to all non-negative $f$ that behaves at least linearly at infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-dimensional symmetry results for semilinear equations and inequalities on half-spaces Beuvin, Nicolas Farina, Alberto Analysis of PDEs We prove new one-dimensional symmetry results for non-negative solutions, possibly unbounded, to the semilinear equation $ -Δu= f(u)$ in the upper half-space $\mathbb{R}^{N}_{+}$. Some Liouville-type theorems are also proven in the case of differential inequalities in $\mathbb{R}^{N}_{+}$, even without imposing any boundary condition. Although subject to dimensional restrictions, our results apply to a broad family of functions $f$. In particular, they apply to all non-negative $f$ that behaves at least linearly at infinity. |
| title | One-dimensional symmetry results for semilinear equations and inequalities on half-spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.08431 |