Rigidity for a semilinear Neumann problem with exponential nonlinearity in the large diffusion limit
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908939664228352 |
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| author | Seo, Juneyoung |
| author_facet | Seo, Juneyoung |
| contents | We consider a semilinear Neumann problem with exponential nonlinearity in a smooth bounded domain $Ω\subset \mathbb{R}^2$. We prove that there exists a threshold $\bar{\varepsilon}>0$ such that for all $\varepsilon>\bar{\varepsilon}$, any classical solution must be constant. This result provides a positive answer to a conjecture recently posed by Calanchi, Ciraolo, and Messina (2026). Our proof relies on a combination of $L^1$-estimates, a Jensen-type argument via the Neumann Green's function to obtain uniform exponential integrability, and elliptic regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04416 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity for a semilinear Neumann problem with exponential nonlinearity in the large diffusion limit Seo, Juneyoung Analysis of PDEs 35J61, 35B45, 35B32 We consider a semilinear Neumann problem with exponential nonlinearity in a smooth bounded domain $Ω\subset \mathbb{R}^2$. We prove that there exists a threshold $\bar{\varepsilon}>0$ such that for all $\varepsilon>\bar{\varepsilon}$, any classical solution must be constant. This result provides a positive answer to a conjecture recently posed by Calanchi, Ciraolo, and Messina (2026). Our proof relies on a combination of $L^1$-estimates, a Jensen-type argument via the Neumann Green's function to obtain uniform exponential integrability, and elliptic regularity. |
| title | Rigidity for a semilinear Neumann problem with exponential nonlinearity in the large diffusion limit |
| topic | Analysis of PDEs 35J61, 35B45, 35B32 |
| url | https://arxiv.org/abs/2604.04416 |