Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912389663817728 |
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| author | Ciani, Simone Gianazza, Ugo Li, Zheng |
| author_facet | Ciani, Simone Gianazza, Ugo Li, Zheng |
| contents | 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 $1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_17926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes Ciani, Simone Gianazza, Ugo Li, Zheng Analysis of PDEs Primary 31B05, 35J25, Secondary 31B15, 35J92 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 $1$. |
| title | Phragmén-Lindelöf-type theorems for functions in Homogeneous De Giorgi Classes |
| topic | Analysis of PDEs Primary 31B05, 35J25, Secondary 31B15, 35J92 |
| url | https://arxiv.org/abs/2505.17926 |