Rigidity for a semilinear Neumann problem with exponential nonlinearity in the large diffusion limit

Juneyoung Seo

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arXiv · 2604.04416

Rigidity for a semilinear Neumann problem with exponential nonlinearity in the large diffusion limit

Juneyoung Seo

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Abstract

We consider a semilinear Neumann problem with exponential nonlinearity in a smooth bounded domain $\Omega \subset \mathbb{R}^2$. 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.

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Juneyoung Seo. 2026-04-06. Rigidity for a semilinear Neumann problem with exponential nonlinearity in the large diffusion limit. https://arxiv.org/abs/2604.04416

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