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

2025/05/23 by Ciani, Simone, Gianazza, Ugo, Li, Zheng
#35J25 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 31B05 #Secondary 31B15

paper · doi:10.48550/arxiv.2505.17926

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∈(0,1) when r→∞. By proper counterexamples, we show that in general we cannot expect α to be 1.

Citations

• Self-improvement of uniform fatness revisited
• Phragmén-Lindelöf theorems and p-harmonic measures for sets near low-dimensional hyperplanes
• NON-LINEAR POTENTIAL THEORY

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