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arXiv · 2505.17926

Phragm\'en-Lindel\"of-type theorems for functions in Homogeneous De Giorgi Classes

Simone Ciani·Ugo Gianazza·Zheng Li
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Abstract

We study Phragm\'en-Lindel\"of-type theorems for functions $u$ in homogeneous De Giorgi classes, and we show that the maximum modulus $\mu_+(r)$ of $u$ has a power-like growth of order $\alpha\in(0,1)$ when $r\to\infty$. By proper counterexamples, we show that in general we cannot expect $\alpha$ to be $1$.

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Simone Ciani, Ugo Gianazza, Zheng Li. 2025-05-23. Phragm\'en-Lindel\"of-type theorems for functions in Homogeneous De Giorgi Classes. https://arxiv.org/abs/2505.17926

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