Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes

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

Publication Details

Journal
ArXiv.org
Published
2025-05-23
Primary Topic
Analytic Number Theory Research
Type
article
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article

Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes

ArXiv.org
Analytic Number Theory Research
article

Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes

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Abstract

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

ArXiv.org
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Analytic Number Theory Research
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Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes · ArXiv.org (2025) | TGRS Research Map | TGRS