Phragmén-Lindelöf Theorems and p-harmonic Measures for Sets Near Low-dimensional Hyperplanes
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- 作者：Niklas L. P. Lundström
- 关键词：Global estimates ; Growth of p ; harmonic functions ; Infinity Laplace ; Phragmén ; Lindelöf ; Subharmonic ; Quasi ; linear
- 刊名：Potential Analysis
- 出版年：2016
- 出版时间：February 2016
- 年：2016
- 卷：44
- 期：2
- 页码：313-330
- 全文大小：331 KB
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1. Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187, Umeå, Sweden - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Potential Theory
Probability Theory and Stochastic Processes
Geometry
Functional Analysis - 出版者：Springer Netherlands
- ISSN：1572-929X
文摘
We prove estimates of a p-harmonic measure, p∈(n−m,∞], for sets in R n which are close to an m-dimensional hyperplane Λ⊂R n , m∈[0,n−1]. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains Ω⊂R n ∖Λ for p-subharmonic functions. Moreover, we give local and global growth estimates for p-harmonic functions, vanishing on sets in R n , which are close to an m-dimensional hyperplane.